Well, Saints row 4 seems to be running the same exact engine as SR3 (and by exact I mean exact), with one major change on PC that elicited a hallelujah from me when booting up the immediately apparently faster Inauguration Station (seriously, even the menus crawled for me in The Third) No more bad optimization. Not sure how many people were affected by 3's usage of hard drive as RAM, but for me this is a big difference. Now I can run it at a stable , bearable framerate on my puny intel Q43/45 express. I could have done so a long time ago, albiet without tesselation, but they don't even make 124 or whatever gig hard drives like mine anymore I think (which is often filled to the utmost brim) never really understood why they'd make SR3 rely on HDD so much...
Still takes a solid 5-10 minutes for me to boot though x.x