I'll agree that I think Saints Row 2 did a lot of things better than Saints Row 3.
SR3 was a very good game, but you get to the top of that game's power fantasy way too quickly and it plateaus very early. Almost immediately I felt like I was at a point where I was only buying upgrades because I didn't have anything better to spend my money on. You get all the best cars, and gear, and guns and then you coast on those for hours and hours and hours.
I've heard people didn't like being forced to do side activities in SR2 but I thought it was great. It gave it almost an RPG feeling -- you'd complete a side quest and equip a new skill, like having infinite stamina or better guns or more followers. Everything had a purpose and there was a strong incentive go for 100% completion.
Saints Row 4 always looked fun (never played it), but it's one of those things where I never really thought of it as a Saints Row game, and they ended up painting themselves in to a corner with it as a result.
I'm not even sure we'll ever see another Saints Row game. Agents of Mayhem definitely seems like it's going for the same audience without all of the Saints Row baggage.
As for being better than Grand Theft Auto... I feel like that was definitely true for GTA4, but for GTA5... ehhh... but that's also kind of a different strokes for different folks situation, too. GTA5 versus even Saints Row 2 are two very different beasts with two very different goals. SR1 and SR2 are natural extensions of GTA:SA and GTA5 breaks new ground in a different direction than that.