Well I've bought a LCD recently although I still have my beloved 19" LG Flatron F900B CRT (flat screen, but CRT nonetheless). I use the CRT on my Windows XP rig (not the one in my sig) mostly to play older games. And it's usually turned off anyway to save some electricity and help a bit with the bill too, that CRT is a beast (and itself consumes probably 2x the energy that the rest of the rig does). Anyway, point is I went from my CRT's native resolution of 1280x1024 to my LCD's (Samsung S23A700D) 1920x1080. When I switched the rig around along with the LCD I also moved most of my games to my "current gaming" rig (the one in my sig, the other one has my older GTX285 and my older Intel E8400, with 4GB DDR). I can say that ultimately "just" the higher resolution itself, by itself, won't do much if the game's own textures were not worked on that much to start with by the developers.
In other words, if you have washed out, blend and blurry 512x512 textures at the game's highest settings and play it at 1024x768, 1280x1024 or 1920x1080 the only thing that it's going to do is it'll stretch out the lack of details further for you to shake your head at when you stare at it. Also, on my LCD (not sure if it applies to all LCDs, I'm kinda new myself to the whole LCD technology since only two months in fact) if I game at any resolution that's not equivalent to my native resolution's ratio then the overall picture (display in general, gaming or not) looks either stretched out horizontal or "compressed" vertically (not sure how to describe it other than it doesn't look "right"). So sometimes I have to "force" myself playing at my native resolution on my LCD with a game that although does support the HD resolution(s) won't exactly do itself justice (I.E. the game's own "best" textures settings aren't HD-friendly to start with).
I mean... playing UT99 at 1920x1080 does not give me "more details" on the textures compared to how said textures look like at 1024x768 (I know, I've tried). But, on my LCD due to the now standardized shape (rectangular) of HD displays I pretty much "have to" play comparably "old" games at my native resolution anyway not "because it gives better details" but simply because otherwise the display looks weird, whereas on my CRT I could be content with a ratio along the lines of 4:3 or 5:3 (say like 1024x768), rather than 16:9 (like HD res). With this said, however, don't get me wrong! There are plenty of recent games (not just released "right now", but recent I.E. from a couple of years ago as well) which certainly benefit from higher resolutions exactly because the devs worked on the textures enough so that when displayed at HD resolutions will "fully reveal" their details as "meant to be" by the developers, probably because first of all they know what they're doing, they're good artists and they probably worked on 2048x2048 textures or something like that.
I mean the better the texture is by itself the more the HD res will display that. But don't expect HD res to "add" detail out of thin air to a texture that doesn't have any details on it to start with.