The difference between III's Liberty City and IV's is that in IV (at least in my opinion), Rockstar Games has tried making every aspect of it as a parody of the American lifestyle and of what New York simply is. Also, let's not mention Rockstar's Easter Eggs scattered all over the map, especially the Hillary Clinton rendition with a cup of coffee in one of her hands, resembling the Statue of Happiness (a parody to the Statue of Liberty).
(https://upload.wikimedia.org/wikipedia/commons/a/a1/Statue_of_Liberty_7.jpg)
(https://pbs.twimg.com/media/CwspradWIAACsOD.jpg:large)(https://pbs.twimg.com/media/CwspqgwWEAYcsJR.jpg)
I think that the part that annoys players about GTA IV is, first of all, the fact that it is poorly optimized, and second, because of Rockstar's humor and the way the flaws of the American life are simply shoved in front of everyone who played the game. I'm not complaining about the story, it was a fantastic one, and both endings were heartbreaking.
Now, let's take a look at GTA III. It's more tame and cartoonish when it comes to the gameplay, pedestrians and/or graphics. I have to admit, it did a brilliant job by grounding the player for shooting in the public (also, the bullets and their traces were so funny and unrealistic). Also, some Easter Eggs were neat, actually.
(http://i.playground.ru/i/88/22/42/00/blog/content/ozsvn9kg.jpg)
Still, they both were awesome games and will bring nostalgia to a lot of players for years to come.