First up, I never played the first Saints Row, so no comparisons from me about that one. Secondly, I have played GTA 4 so I can make the inevitable comparisons.
Before GTA 4 came out, I was so taken in by the immense level of hype surrounding it, and was expecting something that would blow me away (with an RPG). What happened was that it confirmed what we all expected deep-down, that nothing really new or original could be added to the series. The only thing they could add (or try to add), was a sense of realism. This is what, in my opinion, turned GTA from an awesome game into an ok game.
Saints Row 2 changes all that. One word sums this game up from start to finish, fun. Everything about this is about making sure that you, the player, has fun and doesn't have to spend hours driving around the map repeating missions every time you die etc. People have been moaning about the driving/handling in this game, but why? It's arcadey, and matches the game perfectly! If I wanted a realistic driving simulator I'd play Forza/Gran Turismo.
Graphics wise, ok, it's not as good as GTA 4, but again, so what! They're colourful and vibrant, unlike the drab gray-brown that was Liberty City. Glitch-wise, yes this game has glitches, but name one free-roaming game where there aren't any glitches at all. This is easily outweighed by the sheer number of improvements made in this compared to GTA:
When you die you keep your weapons, so no worrying about dying and having to re-stock your arsenal.
Once you put a car in your garage, it will always appear there, no matter where you leave it/what you do with it.
If you die during a mission, it doesn't re-set you back half-way across the game map to have to drive there again.
etc.
But without doubt, the highlight of this game is the co-op mode. Anything you can do in single player, missions, side-missions, whatever, can all be done in co-op. It also works extremely well, and runs very smoothly considering everything that's happening on the screen.
Overall, I believe this is the game that GTA should have been, as it shares much the same fun-ness of Vice City and San Andreas. If you want a serious, well-written gaming experience, then look elsewhere, but if you want to have fun and a laugh with your mates on the (frankly awesome) co-op, then this is the game for you.