I love Saints Row but the missions structure hurt it. Having separate stories for different gangs creates a repetitiveness with the respect system and strongholds. 
I'm not asking for a GTA/RDR style mission line because even that one wasn't great in my eyes either.

I really liked Saint's Row 2's mission structure. I want to be able to jump out/quick save from missions as needed, and it seemed easier to manage than w/GTA.

Not really cause it was all a vehicle for dumb fun anyway. Didn't mind the side mission grinding either cause I'd just turn on the podcast while doing it so I always had more than enough.

With open world missions, I always stick with a particular mission path until completion (or when the game prevents me from continuing). During the GTA III, VC, SA era I would switch between stories and I would always end up forgetting some of the plot points of each mission path.

The way they had it in the original Saints Row was terrible. It basically came down to grinding enough respect to finish off all of the strongholds of whatever gang you were working on at the time; that grinding took it from being a 4-5 hour game to more than 20 hours. Gross.

However, just having beaten SR2 in anticipation of SR3, I can say that I was happy with the sequel's mission structure. Go figure, because it's almost exactly the same, except you get way more respect for side missions. More respect = less grinding. I maxed out a few side missions in about half an hour, and that got me through the entire game. Oh, and the bonuses they gave you for fully completing them were great. Unlimited ammunition for a pair of rapid-fire pistols? Yes, please.

I'm annoyed with a lot in Saints Row. Especially their stupid mini games. Like the whole insurance fraud thing? Yeah, that's cool, for about 60 seconds, then it becomes a horrendous chore. The escort missions were horrendous. The horribly implemented Chop Shop system. With the original game, I tried to grind my way through the missions, only to encounter a glitch that prevented the remaining activities from ever showing up. Complete waste of my time.

Yes I was very annoyed as the side missions pissed me off, like the activities, I wanna be able to do the Activities at my own leisure, dammit! Lucky, Saint Row: The Third fixed that.