I'm honestly not sure. They were both pretty much fantastic, just in... sort of different ways? I think I like Saints Row 3 a little less in Retrospect after having played Saints Row 2, though. While 3 did a little better on the climactic battles and scale of things, 2 felt better during the average missions spent disassembling the rival gangs. Made things feel much better when the time came to actually finish a group off.
I think I have to settle with 2, but if they can combine the mission structure of 2 with the general entertainment throughout 3, I'll be happy.
Saints Row 3 and pretty much every level, although there's something to be said for the design of the world in the second one. I found it weird that even after 30+ hours with that game I was still finding hidden tunnels and shortcuts that hadn't been revealed in any of the missions.
I enjoyed Saints Row 2 quite a lot but found that it just relied way too much on the side activities for longevity/content while also having a pretty lackluster story. I really enjoyed the story missions in Saints Row the Third and found the side missions much more approachable as well. In terms of craziness Saints Row 2 was pretty damn crazy. People who think Saints Row the Third was way over the top probably didn't play Saints Row 2.
Saints Row 2 is better than SRTT in terms of customization and the open world being better, but that isn't enough. The shooting and driving mechanics in The Third are so much more satisfying, and the upgrade system helps with that. You feel a lot less obligated to do the activities, which is good because they decided for some reason to bring back fucking Heli Assault. Also I think The Third is much more well written than SR2.
I liked Saints Row The Third more, I think, and a lot of that is because I was actually able to finish that game. There was a point in Saints Row 2 where I was just suddenly lost interest. I think it's because I had to do more side missions to unlock the next story mission or whatever (I think that's what happened; it's been a while since I've played 2). I also rather liked how utterly ridiculous The Third was. However, I do think that Saints Row The Third was a little too short, and I really missed the amazing amount of customization that Saints Row 2 had when it came to your character's clothes, but overall, I think The Third was better-made game.
The second game just feels like it has more in it. Granted, this doesn't make it the better game, but the only thing in SR3 aside from the main quest that stood out to me was the arena games, where you run through an area and shoot guys. I thought those were pretty fun. However, there was a point in SR3 where I asked myself "What else is there to do around town"? and I looked around the map - and there was not a single thing I cared for. Nothing. I didn't want to do any of the side missions because I'd done all the ones I deemed fun, I didn't want to buy anything because there was nothing left to spend my money on, and I didn't want to screw around much either.
On the other hand, Saints Row 2 has a whole lot of good things to go around. There are more clothing options, more options for a home base or whatever, more character customization options, more vehicle options, more weapons, more upgrades, a lot more side missions (although there are some real stinkers here) and just more. Forgetting all of that, there are three individual main storylines which all take some pretty interesting turns. You'd be hard-pressed to beat SR2 in 20 hours; you'd be hard pressed to get more than 20 hours out of a single SR3 playthrough.
Forgetting the sheer amount of stuff, I have to mention one other thing that I liked about SR2 - restraint. Sounds nuts coming from this series, but the wacky stuff in SR2 actually came across as wacky because the game wasn't wearing a huge clown hat all of the time. It didn't take itself seriously, no, but it never felt like it was trying very, very hard to come across as wacky or weird, and this made the wacky all that more entertaining. It just got tiring in SR3.
No, I do not think that SR3 is a bad game and it is worth your money and time - but Saints Row 2 is a better game.
Shit, I accidentally picked SR 2 when I meant to choose The Third, lol. I wish there was a way to change your vote. SR2 had some great ideas and really found the right direction for the franchise but I played it on the Xbox 360 and the framerate and performance issues rendered the game almost unplayable in parts and really sapped the fun out of it. There were definitely things in SR2 that I wish were in SR:TT, and I hope will return in SR4, but overall I think that SR:TT is a better game.