Having just finished the main missions, I think there's a decent shot Yahtzee will end up liking it. He's not really about side missions (and it's only single-bloody mindedness or the lure of a really good bonus that had anyone complete all of them in SR1 or SR2) and the main missions (once you get by the stupid activities tutorials) is insane. The QTE boss fights will probably lose it points, as any real story beyond "let's do zombies now". Fucking around in the city is just tons and tons of fun, especially as you start unlocking new abilities. I pretty much ignored the main missions until I leveled up into the 40s because I was just having so much fun running around and causing chaos.
Customization... there's three things I ended up missing: being able to customize the Bear, rim spinners and electrical tape pasties. While there weren't as many options this time around, there were far, far, far, far, far, far fewer crappy options.
The Story... while it's a mess, it's a funny mess. The one thing it really needed to do was up the stake between The Boss and Killbane to justify the split ending. Time and time again, when given a choice between revenge and loyalty, The Boss choice loyalty every single time. The "good" ending robs you of a really cool final level, while the "bad" ending requires you to be so hell-bent on revenge against a character who hasn't really hurt you.
Activities... while I don't miss any of the deleted modes, this is by far the biggest disappointment of the game and after playing around with Whored Mode for half an hour, there really was no reason why this shouldn't have been ramped up. I would have used the Professor Genki thing to craft a bunch of wild-ass combat scenario, not just shooting mascots in a booby-trapped liar. You could take some of the bits from the main game such as a rickshaw race, having to achieve objectives while stripped naked and drugged, vehicle fights in virtual reality... or even expand the Guardian Angel activity past the two main mission ones. And there really should be better bonuses for completing them. I'd want to see new weapons and vehicles, not just new gang optimizations.
Saints Row 3 isn't what I wished it had been, but a bit more work on the story and more creativity in the Activities and it could have been. The basic gameplay is improved and the story missions are wonderfully over-the-top.