I'm going to be a contrarian to several people in this thread and say Saints Row 2. You see, I got Saints Row 3 for free a little while back and absolutely fell in love with it, and when I was done getting 100% completion on the base game I was thirsty for more. I'd heard all sorts of good things about SR2 and how SR3 was basically its stripped-down clone. So, I plunked down the $10 at the local used game store and brought home a copy in immaculate condition, complete with the manual and even the little cheat-code insert that originally came with it.
Now, I wasn't expecting the game to be made of gold here: it was over half a decade old, and I was kinda expecting it to look like shit. I did not expect, however, that its primary color scheme would also be reminiscent of fecal matter, with a draw distance so low that I was wondering if it was running on the Dynasty Warriors 3 engine. But I could deal with games with bad graphics(I still use my N64, after all). What I can't deal with, is bad fucking controls. And the controls for SR2 on the Xbox 360 are bad. Not as bad as GTA IV, but still jarringly bad after coming from something with such tight and wonderful controls like SR3. This applies to all control schemes: on-foot controls have asinine ideas like using the "X" button on an Xbox controller to jump(going against every reflex you've developed if you've played anything like Halo, SR3, Crackdown, and most platformers up to that point)and the vehicles don't quite feel great either. I failed many missions over and over due to the really bad controls and cheap AI that took every advantage of your fumbles. On fucking easy, mind you. Aircraft handled even worse, with the ability to flop over and die mere moments after getting off the ground being so common that the Wright Brothers would be laughing the makers of the game's aircraft out of the room.
And then, there's Stilwater. Now, I actually like Steelport quite a bit. It's an absolute joy to drive around in, you can tell where you are in a pinch, with recognizable landmarks all over the city, and the game rarely has a shitstain in the color pallate. It looks reasonably good for its time. Not perfect by any means, and still behind a lot of graphical powerhouses, but still very appealing. Stilwater, on the other hand, stands in stark contrast to that. Driving is a chore in that city, with landmarks being less common than general "themes" for different areas of the city. Now, I do like the fact that there are plenty of interiors in many buildings that populate the city, and they are of pretty decent quality for a game with such a large game map, but that's one of very few advantages I can honestly say it has over its successor, which while they have some real high-quality interiors, they have much, much fewer.
The character customization is also something I found to be more likeable in SR3 as opposed to SR2. You see, it's about quality vs. quantity. Sure, SR2 had a lot more options and sliders for the customization, but as much as I tried I could never make my character exactly as I wanted her. In SR3 however, the outfits were of far superior quality, and I found exactly what I like in terms of style. Yes, I'd like it if I could give my character a small bolero to go with her cute fluffy dress, and make that dress have a satin shader applied to give it some shininess, but I couldn't do that in SR2 either so as far as I'm concerned that's a moot point for the argument for SR2's supposed superiority. Plus, the introduction of jigglebones to dresses/skirts really helps since they actually move more like actual dresses/skirts, as opposed to dress-shaped pants like in SR2.
Finally, the story. I find this one a bit harder to argue, since SR2 does have more impactful moments, like Aisha's death, and it does have a nice feeling of nonlinearity when it comes to taking down and wrestling control from the enemy gangs. However, as I played through the game I began to look at my Saints Boss in a light similar to that of how Tom Hanks saw Woody when he first read the Toy Story script that was revised by Jeffery Katzenberg's orders: Woody in that draft was so mean-spirited, so hostile, and so unlikeable that Tom exclaimed "My character is an asshole!" while recording lines for a test reel. I found the Saints boss to be in a similar light, especially in small moments like when she used her bartender as a bullet shield to save her own hide from the Masako when she first encountered them. Keep in mind, the Bartender was getting flirty with her just moments before being turned into a woman-shaped pile of smoked swiss cheese via a death hail of XM8 rounds and an on-the-spot Molotov. That, and how she treated her homies with such little respect(except for Johnny) made her hard to sympathize with. In Saint's Row 3 and 4 however, the sociopathic element is still there, but you get a feeling that the character actually cares for a few someones, and those would be their homies. They don't act like a sociopathic murderer just for shiggles, but instead they do what they do for their friends, who are more like a chosen family than anything. A puckish rogue, rather than the cold, heartless murderer of the second game in the series.
Now I'm not saying Saints Row 2 is bad. However, I did find it much harder to like than the third.