TheRadBrad uploaded the first 25-ish minutes of Saints Row 4 a few days early, so I decided to watch it.
It really does look like a big improvement from the third. It's even further removed from its roots, but it's not quite as ridiculous in how over-the-top it gets and it doesn't seem to be trying to cram as many crazy shit into every frame. It actually feels more grounded and serious even though it's still an exaggerated parody of a game because it's much more coherent in what it's trying to do, rather than the "Throw everything and hope it sticks" of the previous game. The actual jokes are a tad bit more subtle, such as the intro being a Zero Dark Thirty parody without ever actually referencing it until you see the "Mission Complete" at the end; most of the parody is in how your character is locked into the "Crouch walk forward" animation and uses his knife a lot.
The combat also seems a bit improved. The animation-to-ragdoll transitions are much better, so you've got generally smoother death animations and greater variation than either canned animation or plain ragdolls. Melee combat appears to be a bit more varied than just wrestling moves and nut punches.
That said, the combat is still very much the same thing that it has been since the first game. It feels a bit sad when you see the Boss in one of the first cutscenes doing a perfectly choreographed action movie fight sequence with guns, fists, and cars that would be really fun to play, and then the actual fighting is "Run forward and hold down the trigger on a submachine gun until the guys die."