The main difference between GTA III on PlayStation 2 and GTA III on phones and tablets is the controls. The rest of the game remains pretty much exactly as it used to be, but it does take a while before you will be fully comfortable with the on foot and driving controls present in this version.
The game uses much the same controls as all the other sandbox action games designed for touch screen devices. You do have a lot more choice than in most games, however, as you are able to change the position and size of all the on screen HUD elements. Make sure you do this to get a set up that you are comfortable with.
The on foot controls are very simple, and work well for the most part. You can tap the door icon to enter and exit vehicles, the fist or weapon icon to attack enemies, and there are similarly self-explanatory icons for jumping, running and interacting with other objects. The difficulty comes with shooting, as the game's targeting system can be a trial, and it is very hard to snipe enemies quickly.
You have the choice of using analog or digital steering. Analog allows you to touch on an on screen circle to choose the direction that you want to drive in, and is much more flexible than the default option. Your choice here really depends on the size of the screen on your device, as you need a bit of space to be able to use the analog steering circle.