Take this lightly as I've only watched the ever so lovely Jesse Cox play both of them, but 3 is defiantly a winner for more. The overall reason with that is that 3 is basically Saints Row 2 on cocaine, but Saints Row 4 is 3 on several lorries worth of cocaine snorted through a vacuum cleaner attached to all holes in your body.
In 3, you could get super powers. They existed for a mission or two and were AWESOME. It was a HUGE way to ramp up the action as you are suddenly super speeding your way to save a homie. But in 4 you have them the hole game, so not only do they get old, but they remove any reason to ever use a car, helicopter or plane, or even walk. Basically it turns the city into an annoying thing you jump over to get to the next rooftop.
If there were two main reasons I'd say 4 is worse is that the enemies were just boring. In Saints Row 3, enemies arrive in cars, helicopters, on foot and other such methods. All fun to watch, fun to explode and result in long chases. In 4, enemies arrive in small bubbles that they just keep jumping through until you shoot them. And that's it. I don't think they even have any vehicles, only the virtual police have some weird hover cars. Plus, all the enemies ended up either being really easy to murder and not remotely dangerous, or immune to everything and as tanky as an Abrams jacked up on tank-morphine.
The second is the mission structure was just weird. You almost always returned to your little ship in space after a mission, so it worked as a sort of hub. However, all of the missions were rather crap and boring. See, the first few missions were awesome. The recruitment and loyalty missions were awesome, and the ending was awesome. But everything in between was so, so boring. The missions consisted of mainly normal tasks. So, Kinsie would tell you to do a side mission (that you normally do while running around the city for extra dosh) and make up a weird story reason, then tell you to go to the next mission, then kill 10 zin, then go to the next side mission.
So basically, the middle of the game is taken up by a random homie telling you to do side quests, and then giving you a reward. No, no set pieces, no scripted missions, just a main story telling you to do side quests. It was kind of saddening.
So yeah - huge rant just to say, Saint's Row 4 is awesome, but Saint's Row 3 is so much better.