Both have their pros and cons, but I ultimately prefer PC.
Pros for PC:
1. More customizable
2. You can do multiple things at the same time (e.g. Music)
3. Mouse and Keyboard is a better setup for strategy and FPS games, since you can quickly aim/move your cursor.
4. You don't need disks for every single game you play
5. Text Chat with friends is easier
6. Can be potentially stronger than Xbox or PS3, if you're willing to put a lot of money and effort into it
7. Closer to the screen, so it's easier to read subtitles or notice small cameos or details
8. You can do things such as writing papers or making posters and then you can hop onto a game without having to move around the house
9. Portable Gaming Laptops. 'Nuff said.
Cons for PC:
1. Installing games can take a while
2. Can get uncomfortable if you have a cheap chair
3. You're more vulnerable to viruses or intruders (yes, you run the risk when using Consoles, too)
4. Notifications, such as Facebook, E-Mail, IM, or Anti-Virus, can get in the way.
5. It can be pretty expensive if you're looking for a top-notch Gaming desktop
Nutshell for PC: The Cons can be easily solved, which are just little picky things. I prefer PC, but that doesn't mean Console Gaming is terrible.
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Pros for Console:
1. You can get comfortable on a sofa or lounge chair
2. Controls take less time to get used to
3. Graphics and Processors are generally good when you first buy it
4. Current-Gen consoles cost less than Gaming PCs
Cons for Console:
1. Typing or Text Chat is time consuming and sometimes annoying
2. Since wireless controllers are the norm, you might need to constantly change the batteries
3. To change games, you need to get up, grab the disk, and replace it
4. You're far away from the screen (usually), so you might not be able to read subtitles or hear it very well.
5. Consoles are games and games only, which can be less convenient if you were taking a quick break
6. You don't really have a say in what the developers do with the console. If there's a bad layout change, you usually can't change it back
7. You are very restricted when it comes to customization
Nutshell for Console: I never really liked Consoles. If you have bad eyesight, like me, it can be hard to see the screen. I also went through like 2 packs of batteries keeping my Xbox controller alive. It's good for when you're playing with family, but if you're by yourself, it really seems impractical, since a lot of the good games are on PC anyways