In a gaming aspect:
PC
Pros: Plays games well
You have mouse for precision and you can also use a controller
You can do other things while gaming
You can change the parts easier thus you can upgrade without having to buy a whole new computer
There are SOME exclusive games you can get via the internet and steam
Cons: You can't always insure that games will run on it
One day, your PC WILL get old and you'll need to upgrade it
Higher price than console
Console:
Pros: The games will always play so long as they're in good conditions, no system requirements (other than memory)
Gameplay is always smooth (offline)
Two words: Console exclusives
Lesser price than the PC and still plays the same(ish) games
Controllers are made for the games it plays
Cons: Console may have a lesser time of use length
You can't just upgrade the parts, you have to buy a whole new console
Internet games you MAY need to pay for (Xbox)
They both have their pros and cons. PC in the gaming aspect is basically a gaming console.