I'm the same as Action, screw the missions, i just wanna destroy as much stuff as possible before dying. Or trying to outrun the cops as long as i can, while only staying in cinematic mode. I've only really had one day with GTA4 so i can't really say how good the missions even are, but i do like the cover system they have, and better police AI.
I once tried to get 6 stars by blowing stuff up. I got to 5 stars and blew up a ton of helicopters with the rocket launcher but unfortunately, the last one I blew up crashed down on top of me and smashed me.

Now if you want to explore the city freely without the 6 stars, you need to do the missions until you unlock all of it. I beat the game first and then went on mass rampages of doom.
Here is some fun stuff I like to do.
1. Use a cheat code to get the military helicopter and fly my friends around the city. I sometimes even fly my dates around the city to avoid the traffic.
2. When the cops are chasing me, I jump into the water ans swim away. THis does not work if you have 3 or more stars because they will just send a gun boat after you. If there is no water, I lose them in a subway tunnel.
3. I like to punch some random guy and when he chases me to beat me up, I find a cop and let the guy hit me in front of the police. The police then beat the crap out of him.
4. I sometimes call 911 and when the cops get there, I jack the police car and use it to pull people over or make them get out of my way.
And just a little side note for those actually doing the missions. Spoilers ahead!
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When you get to the part where you get the option of killing Dimitri or making a deal with him, go for revenge. I'm not telling what happens. Just that it is better than making a deal with him.
I'd say the Driver series is better.
I haven't played GTA.
How do you know it is better than GTA if you haven't played GTA?