****SPOILERS*******
Excuse me while I ramble...
I'm on PC and I 100% Vice City months before I bought GTAIII. For starters, GTAIII surprised me with its capture of New York City to a "T" and its massive size that has to be bigger than Vice, but definetely has more layers to it transportation (not in vehicles, however) wise - with the dam, bridges, elevated highways, trains, subways. Of course, this has an unfortunate downfall as there's no 'you are here' map to guide you through this intricate maze of roads that especially poses a problem when there's usually only one way to get places where as in Vice there were numerous - hell there was only 2 islands and 4 bridges, but Liberty has 3 islands and only 2 bridges between them both (subway's too much of a pain to find and use). Gameplay would be so much more enjoyable if they designed an interactive map.

So, you have to explore the roads yourself which are no fun as by this point in the game the nameless, voiceless thug you control has pissed off every gang on the board that they shoot you on site with powerful weaponry and respawn capabilities. Great AI design guys! Now, that I finished the missions on Portland, I avoid it like the plague now.

Still can't get over how I managed to get on the Leone Family's bad side. Some dumb ass floozie, Maria, gets picked up by you and you run her little bitch errands and of course this horror of a girl is cheating on the Mafia with the Yakuza's and she gets caught and for some random reason she hooks you up with her betrayal so now you have to wipe out the coolest guy you worked with and now will be shot on site when you enter their territory. Good thing they carry the most powerful weapons known to the game. Similarily, my favorite was when they had me kill a crimelord that you were actually tight with simply to help some industrial mogul get top dollar for his property.
I guess, what it all comes down to is the motivation behind the character your playing. In Vice, we knew were on the road to controlling the town, but in Liberty I have know clue why I'm doing half the stuff I'm being sent on.
At least, in Vice you had reasons behind attacking gangs and where ultimately trying to control territory. Also, I never had gangs shoot me on site after missions in Vice. The Haitians were out for me, but that was simply because I made it a point to provoke them off-mission. Again, Vice only had the 2 gangs, where as the whole GTAIII world is controlled by gangs.
You still have the standard foolish reasons and storyline cliches to go on your missions in both Vice and Liberty, so there really was no difference there. Good thing the missions were fun, I found myself skipping through the cutscenes just to avoid confusion. But GTAIII had some missions that really crossed the line in confusion. For instance, you have to collect gang cars, but they don't bother to tell you which cars to pick up so you run on a wild goose chase to first try to remember what gang cars exist and where to find them and then some won't even be accepted after all that. Worst Mission Ever.
There are some other minor complaints. The radio stations are similar to the sound of those in Vice, although Vice had much better selection. Liberty has limited options geared mostly to urban youth with rap, mix/dance, jamaican, etc. I was a little offended that they had no alternative rock which was huge in the mid-90s. The in-game sound effects ultimately are limited as well as all you are able to hear are honking of cars and the ricochets of bullets bouncing off your vehicle when you drive through the neighborhoods of all the gangs you've pissed off. I find that I have to turn off the sound all together just to bear it.
Don't get me wrong though, the game does kick ass. It's just for the above listed reasons, its hard to play it for very long before I get frustrated and have to put it down. Something to does make it more bearable than Vice, was the control of cars. In Vice there was no practical cheat that improved car handling, but in Liberty the cheat available is very helpful especially since it allows you to boost (similar to the taxi boost in Vice) which is helpful to maneuver the crowded maze-like streets of Liberty. There isn't much more cheats however and I would've loved to have the boat-car cheat so you can not be afraid of constantly falling in the many waters that exist everywhere in Liberty.
So, all in all, it's a great game that is only limited by some major flaws that shock me still as to how they slipped by the creators (I'm sure it came down to deadline and budget, though): interactive map and gang AI behavior being the principle faults.
But knowing the frustrations and the fact that there is no 100% prize at the end, I will stop playing after the missions are through and not spend the months 100% this game like I did Vice (which was a bit disappointing when you did - the rewards were a bit meager).