I vastly preferred Saints Row 3 and 4 to the first two which were poor GTA rip offs to me (the second one also tried too hard to be edgy) with no unique identity. SR3 and 4 were at least pretty fun.
I think a Saints Row 3 esque games with a better open world would be a good balance.
I feel the opposite, SR2 felt so much better than SR3 to me. Things like FUZZ and Fight Club were simple yet enjoyable minigames that SR3 lacked. Things like the ability to layer clothing may be small, but they were great when you wanted to make wacky clothing combinations. Stilwater was much better than Steelport as well, much more environment diversity.
How edgy the games were is debatable. Personally I enjoyed the cutscene were the Boss kills Julius, it showed how much Julius underestimated the Boss's power lust in SR1 even if he did try to blow them up on the boat at the end.