Well, really Saints Row 4 was supposed to be an expansion to The Third entitled "Enter the Dominatrix". But they felt the concepts they were going to introduce were far beyond what they had intended, and decided to flesh out an entire game out of it (And dropping the titular Dominatrix entirely).
Considering how ass The Thirds DLC missions (Gangsters in Space was amusing I guess. But the one with Hulk Johnny Gat and Aisha can fuck off, and Genki's is barely worth mentioning) are I can't help but feel a little jipped in that regard.

Still, they dropped the rideable raptors and dragons from the experience.

Which I guess holds 4 back. Those would've been nice, even if the super powers make stuff like that kinda pointless.

I'm not sure how accurate to the original design the DLC for 4 is. But I don't see them making bullshit up.

Also I finally got around to finishing Gat out of Hell. It was okay. But the gun you get for killing Dex 7 times makes the final boss a cakewalk. Though I quite liked the flying mechanics after I got used to them.

Also, you know. Aliens > Zombies. The Thirds Zombie Island was so shit.