The "golden rule" is an HDTV is only as good as the video it receives. Cheapskates will get the kind of poor results LCDs are stereotyped about.

There's two key faults in a typical LCD retro gaming setup:
Poor scaler.
Using composite/RF on consoles capable of better.

Together these may cause very fuzzy images. Most LCD screen panels are themselves actually decent quality, that can be demonstrated with trying HD content on them.

XRGB type up-converters reduce the former by offering improved scaling to the TV's HD level. Component or RGB cables/mods reduce the latter by letting the consoles provide cleaner source video.

Component for the PS2 works well. It's near identical quality to RGB, except component mode allows 480p in compatible games. Careful though! Often the normal component input of HDTVs won't accept low-res games (like PS1 or Disgaea/ICO). Even if they will by s-video. Leading to an annoying cable switch on some TVs if your collection has both 480p games and PS1 games.