Advantage of console:

Buy one and it will be fine for a long time (see Playstation 2). As the hardware does not change you can really optimize your games for the hardware. Thus you don't have to improve the hardware performance, you optimize the software for the hardware.

Advantage of PC

• Mouse and Keyboard are more exact than any gamepad. Some games are just impossible to play with gamepad.
• strategy games mostly, also ego shooters and also economic simulations are way better to play on a PC with mouse and keyboard.
• with a PC I can also do other things than playing. Like easily answering questions in a forum or writing a letter, doing a powerpoint presentation ... etc.

Advantage: PC games end up being cheaper

...because:

1. The prices drop faster in the months after initial release
2. There are more demos for PC titles, so you spend more time playing those (though this is changing)
3. (For some people) piracy is easier (not that I endorse this)
4. Steam sales

Advantage of console:
- games are compatible. When you buy a game, you know that the game will work on the console.
- You can turn it on and start playing. You can access friends without having a separate program. (exception to Steam) - You don't have to install. You wont have to worry about running out of hard drive space on a console if you have many games.

Disadvantage: PC hardware is more expensive than the console equivalent

(Meaning to run the same game with equivalent visual quality/speed, the PC costs more than the console)

Although, someone once pointed out to me that if you already have a newish PC, buying a decent video card is cheaper than buying a console (which is why I'm mainly a PC gamer at the moment, myself - I needed a new PC anyway, so I just added a good GPU).

Disadvantage of consoles:
- limited game choice.
- for the most part mods not allowed.
- mostly $10 more expensive than PC games. When new.