This game doesn't take itself seriously, but that doesn't mean you shouldn't.
SR3 is a hoot, everything about it is over-the-top and absurd. It's been a while since I have played a game that didn't stress me out and allowed me to just have some silly obnoxious fun.
You begin the game taking part in a heist gone crazy as a member of a street gang. After the opening mission you get to create a character that can be as cool or ridiculous as you desire. Wanna be a badass? wanna be a zombie? wanna be an obese silver-skinned man with a purple afro and a woman's voice? You can be just about anything you want to be. If at any time you feel like changing yourself completely you can visit one of the many surgeons in town to do so. Customization is a huge part of the game and one of its strengths.
So let's break things down:
Gameplay: It plays much like GTA but the controls are sharper in my opinion. Driving and combat is a breeze and you never feel out of control. The variety of activities available is a breath of fresh air. Want to play in traffic? Want to save whores from their pimps? Want to fall out of a plane in a Tank? you can do pretty much anything.
Graphics: Nothing special but not bad. The city is fairly large and load times are fast.
Sound: One of the better soundtracks around. Great music from recognizable artists and even an Adult Swim radio channel. The voice acting is great and the dialogue is hilarious.
Story: The story is advanced whenever you want to start the next mission so if you want to buy up property or bust up rival gang activity before continuing the story you can. When you do get around to the story it is pretty outrageous. The characters are memorable and the situations are priceless. Some missions give you a choice on how you complete them which changes the narrative.
Overall: The game is just plain fun. If you are looking for a casual game to mess around with and laugh then this is the game for you.