I recently went through this after trying to decide which premium site to go to, so I thought I'd share my findings.
PlayChess: ChessBase's site.
Pros:
-the site automatically interfaces with ChessBase database, Fritz and presumably most of ChessBase's software. It's just convenient to easily flip between the database and the site.
-slick interface. the interface is extremely simple to use and quite nice. there's an entertaining little geo-locator that shows your rough geographic location as well as everybody else's so you can see if there's any other PlayChess players playing very close to you.
-lots of players! the site has significantly more players than ICC.
Cons:
-no sort of automated match making system. you're forced to manually seek out challenges and hope somebody accepts.
-the average player is quite weak. it does have way more than players than ICC, but it seems that every single German is given a PlayChess account at birth. ChessBase is a German company and there's some sort of nationalism going on here. I had a hard time getting games against strong players. I'm not entirely sure why this was as there are plenty of GM's and others that make this their home site, but this is what I encountered.
-very minimal chat. this could definitely be a pro depending on how you look at it!
ICC provides a more IRCish interface. PlayChess is there almost exclusively to well... play chess. ICC is more about playing chess and chat.
-no sort of free training available. on ICC there are countless free lectures/etc available. PlayChess has a wide variety of archived lectures and other topics available on demand, but they all cost $.
ICC: A private company that, as far as I know, was the first major pay-to-play chess site.
Pros:
-strong players! first and foremost. there are tons of very strong players on ICC constantly playing. about 25% of my games on ICC are against FM/IM/GMs which is just extremely good for learning and improving.
-automated match making. Just type "5" or "15" and you'll be paired with a comparably rated player in a 5 0 or 15 0 game very quickly. As a small downside, the 15-min pool is very weak. After playing 10 games I did not face a single player who would have been above ~1800 USCF. The 5-min pool is full of very strong players and where I put the vast majority of my play in.
-lots of free training. ICC constantly has free lectures, strong masters analyzing live games, etc.
-chat! ICC has hundreds of populated chat channels on every topic from opening theory to politics to philosophy. I'd recommend avoiding the politics channel though. The subset of chess eccentrics with political eccentrics is a really scary group.
Cons:
-Terrible interfaces. There are two primary interfaces available. Blitzin and Dasher. Blitzin is the older interface and is normally quite nice, but when I used it on vista there piece set was low resolution and blurry with no apparent way to fix it. This was not a problem when I played a couple of years ago (on XP). But either way, it rendered it unusable under vista, and their only support was unable to help.
The other interface is Dasher. It looks much nicer, but it's extremely annoying. Absolutely everything pops up in a window. If you want to finger somebody (look at their rating/etc), it pops up in a new window. If you want to see what games somebody has played recently, it pops up in a new window. Even the chat channels are all in a new window with tabs for each channel. It's also poorly programmed. If you are logging your games to a database (as it can automatically do), and have said database open when you complete a game then the program will crash. This happens to me constantly as I look through my games after playing them in my database and often forget to close it before starting a new game.
-Fewer players than PlayChess. This should mean a smaller playing pool, but in my experience there is a substantially wide playing pool at higher ratings.
-The server can be somewhat unreliable. They tend to do things like server maintenance while the server is running. This lags everybody to no end, and can often result in disconnecting/forfeiting games, etc. And I tend to get disconnected from the site fairly frequently (about once every 2-3 hours). That said, I'm playing from Thailand, but I had the same problem when playing from the states.
Both Sites:
Both sites have plenty of additional offerings like tournaments (sometimes for real money prizes), private chess coaching and a wide variety of chess variants such as bughouse.