I was and am a GTA player that enjoys doing missions in various ways. For example in GTAIII a lot of the biggest missions are your own sandbox. The game gives you a goal, for example, assassinating Salvatore, and it's up to the player to use their creativity to accomplish that. Missions have tiers to them. There's one element, like Salvatore walking to his car. You could use that opportunity to snipe him. There's a roof top with stairs across from Luigi's club (Sex Club 7, I can still remember that because that game is embedded into my brain) that allows you to do just this. You could wait until he gets in his car and fire a rocket missile at it if you have that weapon. But he also has an entourage and as soon as he gets in his car, there's a chase, which is the second tier of the mission.
Personally, I find Salvatore gets in his car took quick to snipe, so what I like to do is take a few cars and bar the exit to the alley. Salvatore can't get out because AI in GTA3 can't get into cars unless otherwise scripted to do so (for example, if you're inside it or it's the car they're supposed to get into). So the AI will be stuck in an endless loop because there's an obstacle. This is when I take the opportunity to climb the roof top and snipe him. I take the shot and speed off in a conveniently parked getaway car. Others might just assassinate point blank in front of his face. With enough armor to survive his goons it might be possible.
My absolute favorite open ended GTA moment is the final mission of Vice City. After you kill Lance you're on the roof of the mansion. There's guards below but they're easy to take out. I like to jump off the mansion roof, get into my garage, drive my car into the front door and run over the final boss, winning the mission.
GTA allowed that kind of freedom. The missions (not all of them of course) were fairly open-ended if you had the creativity to see it through.
GTAIV promised to expand upon this more than ever before. Previews suggested a Hitman-esque amount of freedom to how you commit missions. Instead what we got were some of the most plain jane, linear, creatively defunt missions in GTA history. What an utterly disappointing game.