PS2 games are mostly output in 480i (480 pixels of vertical resolution, with 240 pixels painted each frame; first the even lines, and then on the next frame the odd ones). In between frames the game image is updated, so when there is lots of motion the odd and even lines will show significantly different views. But because CRT pixels fade quickly, you almost never see the disagreement. Because LCDs have high persistence the even and odd lines are visible at the same time, and when there is lots of motion the result is ugly. If you happen to have a PS2 game that supports 480p (progressive, as in not interlaced), put in that mode and everything will look a lot better on your LCD.
The other issue is that the PS2s doesn't do anti-aliasing by default so sharp edges can look pixelated on an LCD. This is particularly bad in 3D games, and not so much of an issue in 2D games (of course, >90% of games are 3D). On a CRT this issue is partially hidden by the fact that image is blurred a bit by TVs hardware (unavoidably). This blurring is due to the amplifier that drives the cathode ray which cannot make large transitions (say, black to white) instantaneously, and thus spreads the change over a couple pixels. Small changes in brightness/color require less change in the amplifier gain, and thus are displayed more faithfully. This is exactly what you want for a "low-fi" antialiasing . You could turn down sharpness on your LCD display, but that will make everything blurry, which is crappy antialiasing.
I realize this post would be 10 times better with pictures, but it turns out to be nearly impossible to take representative photos of an actual LCD or CRT. So I'll just give my personal experiences, from best to worst.
PS3 with PS2 hardwareEarly (launch) PS3s can play PS2 because they have most (or all) of the PS2 hardware built in. The PS3 has HDMI out, and if you plug that into an HD TV you can select up to 1920x1080p as the output resolution. The PS3 doesn't do any magic at the PS2 level though - it just runs the ps2 hardware's 480i output through a built-in deinterlacer and upscaler. I found the output to be noticeably blurry, independent of settings. But interlacing artifacts basically disappeared, and aliasing was very low, because of the blur.
Both HDMI and YPbPr are supported. HDMI worked the best; I found that 720p and 1080p over YPbPr were not recognised correctly by my iScan HD+. Interestingly, you can use HDMI for video output and still use the sony "MultiAV" to output audio over RCA plugs. Handy if you are connecting to a computer LCD which does not support HDMI audio.
The PS3 will also work with games that support 480p, with sharper output presumably. Note that in the one case I tried, shadow of the colossus, 480p didn't actually look clearly better, and in some ways worse. But I find that hard to believe and presume it was entirely an anomaly.
Some downsides to the PS3 are: no built in way to plug your PS2 controllers in, and no built in way to use your PS2 memory cards (to transfer old save files). It appears that adapters exist for both of these issues. I'd be interested in suggestions in the comments section below.
The other big downside is that launch PS3s are hard to find, and have a reputation for dubious longevity. I don't know how true that is. A real ps2 costs about $20 on craigslist, and if it breaks, just get another. There's also the question of how compatible the PS3 is with ps2 games. Not all of them work, esp. if you buy the version that only has part of the ps2 hardware built in. Wikipedia has a fairly exhaustive list, and it seems that significantly more than half do work.
The big upside is you also have a PS3 out of the deal :-) It also plays PS1 games, just like the PS2.
Cost $600 in 2006, and now at least $100 used, probably more.
DVDO iScan HD+The HD+ clearly had the sharpest image of all the solutions I tried. There is a clear tradeoff however, because some of the interlacing also made it through, and there was another artifact, which shows up when there's a lot of motion - sharp edges appear blocky because in areas of high motion the HD+ eliminates interlacing by just doing line doubling. I think the algorithm is basically as follows: When the scene is essentially static, concatenate the first and second field together such that all of the 480i pixels are visible simultaneously. When motion exceeds a threshold, show just a single field at a time,(240 pixels, stretched vertically to fill the screen). This might sound horrible, but in practice it looks ok because it only applies it to regions with high motion. So the status bar, for instance, will stay sharp the whole time. This effect is somewhat masked by motion blur, but if the lines are high contrast enough (such as a black tile floor with white grout) it's quite visible.
The other issue with the HD+ is that its default level of sharpening is too high, highlighting the lack of hardware antialiasing on the PS2. Unfortunately, they do not let you change the sharpness setting if you use the YPbPr input, which unfortunately is necessary to get the best PS2 image. To adjust sharpness you have to use composite which looks awful on the PS2, or S-Video, which looks ok except that color resolution is halved (but hey, that's not clearly bad since it helps with the aliasing). Another way to reduce the sharpness somewhat is to set the output to less than your panel's native resolution. Here the HD+ shines. It supports 20+ resolutions and then you can tweak them in single pixel increments to create resolution never before seen by man (or at least your LCD). Pro gear can be fun sometimes.
The HD+ plus supports pretty much every analog input known to man, and also lots of video formats including 480p, which makes for zero interlacing artifacts. Doesn't help with the aliasing issue tho.
The HD+ was made in the mid-2000s, and cost $1500 new. Now they go for less than $200 on ebay. It's clearly a premium device with loads of settings. It also has an extremely unintuitive interface, at least if you use the front panel (I don't have the remote). I was disappointed to find that the used one I purchased had extremely blurred & streaked VGA output suggesting that the analog display path had started to fail. There are some risks in paying $200 for a 10+ year old device.
DVDO iScan Pro
The iScan Pro output seemed "muddy". Not a technical term, I'm aware. Something like blurry and low contrast combined with a little bit of noise. Now, that sounds awful, but there are some distinct upsides. Interlacing was virtually invisible (on par with the PS3), and the lack of antialiasing was also well masked, and it's a bit sharper looking than the PS3. Though it is quite a bit older than the HD+, I find myself preferring it in games that are prone to aliasing problems. It's also dead simple to adjust - just a set of 6 knobs on the front for sharpness, brightness, etc. It has the same gotcha as the HD+ for YPrBr input though - you can't adjust the sharpness. Since it's an older device, it doesn't support anything other than 480i on the input side, though it does support YPrBr, composite, or S-Video. It only outputs 480p over VGA, letting your LCD do the upscaling. Which seems to be fine.
Not supporting 480p is a real bummer though, since that really improves the appearance of the games (zero interlacing issues, which is after all most of the reason for this post in the first place). Perhaps your TV has decent support for 480p and you can just switch cables depending on the game. Or have two PS2s, they are that cheap after all.
The Iscan Pro was about $1000 in 2000, and now goes for around $100 on ebay.
LKV7000 / HD Box / GBS8220
The final choice; both cheapest and something you can still buy new. The output looks kind of like the iScan Pro, but even muddier. Aliasing issues were masked very well, but interlacing was still visible at times, unlike the iScan Pro. Not so often as to be a problem, but definitely noticeable during high motion. I used this device for a year, and I got very used to it, so for the price it's a pretty good option, but it's also clearly the least good. Plus, mine has a strange green cast which I've occasionally heard other people complain about. Not clear if it's an intermittent manufacturing issue, or a universal problem that not everybody notices. It only supports YPbPr input, but that's fine for PS2 users. It supports 480p, and looks really good in that mode (better than the iScan Pro on 480i for sure). You can combine the two devices somewhat easily, because the LKV7000 has VGA passthru that is active when the YPbPr cable has no signal, but you'll need two PS2s, or to swap cables.
The interface is also horrible. 3 hard to reach buttons on the back that don't properly debounce, so when you push one once you get anywhere from 0 (oops didn't press hard enough) to 4 effective button presses. Once you've found the settings you like, there's not much need to change them, though sometimes I like tweaking the sharpness.
I can confidently say that the LKV7000 is the least good solution, though not without merit. While I claimed the list above was ranked from best to worst, it's not entirely true because the ideal device depends at least some on the game. For instance, Shadow of the Colossus has horrible aliasing. It looks best on the iScan pro for that reason, with the LKV7000 coming in second. The HD+ highlights the aliasing to a painful degree, while the PS3 is somewhere in the middle. For Jak II, the PS3 is good, but is definitely soft looking, whereas the HD+ keeps everything sharp and the interlacing issues are minimal (and eliminated if you switch to 480p). Of the devices, the HD+ certainly offers the most options, tweaks, and supported formats, so I'd probably go with it, except that the PS3 is cheaper and plays PS3 games. So really it's a toss up.
Except for this: none of these solutions look as good as a CRT. If you can, go that route. It's a shame that now that we have high speed LCDs (240hz according to marketing, at least) that we can't just emulate the interlaced display of a CRT properly, and display 480i as interlaced pixels, drawing half the screen at a time and leaving the alternate lines black.
Finally, I would like to acknowledge that all of this blather is in some sense derivative of http://retrogaming.hazard-city.de/, which reviewed all this equipment too (that's how I found out about these devices in the first place). The opinions here all mine, however, and are based on my actual experiences, offering a 2nd datapoint from fudoh's.