If your concerend with PS1 compatibility, get the black one. The silver slim has some sort of issue playing certain ps1 games. The list isnt huge, but its still a much bigger list than the black slim has.
*EDIT* It has problems with a few PS2 games as well. Heres an old article from IGN about it.
http://ps2.ign.com/articles/659/659949p1.html
The slim model PS2 will be seeing a new color over in Japan to coincide with the holiday sales season, Sony Computer Entertainment announced today. Starting 11/23, consumers in Japan will be able to purchase the Satin Silver PS2, model SCPH-75000 SSS. The system will include a satin silver Dual Shock 2, a satin silver vertical stand, AV cables and an AC adapter, and is being priced given open pricing.
SCE will also make available on 11/23 Satin Silver versions of the Dual Shock 2 controller and PlayStation 2 Memory Card. Both accessories will be sold for 2,940 yen.
The conventional slim PS2 model, known affectionately as the PSTwo, has product number SCPH-70000. When releasing new color variations, Sony usually keeps the product number the same but tacks on a few letters to indicate the new color. With the new Satin Silver model, though, Sony has switched to a completely new model number.
It turns out that the Satin Silver model, while having the same functionality as a standard PS2, has problems running certain PlayStation 2 and PlayStation titles. The exact list of games with problems is available, in Japanese,
here. Here's an English list of PS2 games that won't run properly on the Satin Silver unit:
Gauntlet Dark Legacy: Will sometimes freeze following the opening movie
The Stylish Mahjong: Will sometimes freeze at the save screen once you've changed the options
Racing Battle C1 Grand Prix: sound effects will sometimes replay endlessly when you hit walls and rails
F1 2001: will sometimes freeze after the title logo
F1 2002: will sometimes freeze after title logo when game is started up with GT-FORCE controller attached. If GT-FORCE is not attached, works fine.
Hitman Contract: takes extended time to create save file
Tekken 5: When selecting "Tekken 3" from Arcade History, the game will sometimes freeze following the save screen.
The PS2 list isn't too long, but the PlayStation list, in comparison, includes nearly forty titles. Most of these are smaller games, but Resident Evil 2 apparently has some sound problems during movies.
All new PlayStation 2 revisions from here on out, including any units that carry the SCPH-75000 model number, will have these problems. Sony hasn't provided a reason for why the problems exist, but suggests that those who want to play the blacklisted games purchase an SCPH-70000 or earlier model PS2.