Apart from the removed features, the garish graphics, the bland city, the poor plot development, the lack of character motivation, and the lack of reason to explore... I think one of the main reasons I thought Saints Row: The Third and Saints Row IV were poor sequels is the missing time between the games.
We've had discussions in the Saints Row Wiki Chat regarding how much better Saints Row IV would have been if the prologue hadn't been so rushed and we'd gotten to take part more of the backstory, but I'd never considered it in the context of why I didn't like the game very much.
In Saints Row 2, you have been in a coma for *cough* years, so it's perfectly explained why you're out of the loop while the world has changed so much without you. The first mission makes sense, and the entire game has a purpose: retake the city.
After having controlled, or at least witnessed, Playa's every waking moment for the first 2 games, there is a jarring disconnect in The Third.
In Saints Row: The Third, exactly what you've been up to during those *cough* years is never really explained, apart from selling out. We got hints of what Pierce and Shaundi were up to, but not Gat and Playa. This first mission makes no sense, and I spent the entire game asking "Why am I doing this again?".
- Better storyline: The Saints are already broke due to reckless spending, and try to rob a bank in an unfamiliar city, and Loren takes control of the bankrupt Saints/Ultor group as payback. (Explaining why the Saints don't already own all Planet Saints stores.)
Saints Row IV is even worse, given that there is 5 years between the first mission and the next.
- It would have made more sense if it began without explanation in Pleasantville, with the missing time was handwaved by "aliens". Having Playa become President is a completely gratuitous and unnecessary plot point: Zinyak abducted Gat just for being a badass, so it stands to reason he would also abduct Playa for the same reason.
This 5 years, btw, is the first time the amount of time which has passed has ever been mentioned in game. But we still don't know the amount of time between Three Way and Zero Saints Thirty. Clearly at least several months, possibly several years, given Matt Miller's aging.
Saints Row and Saints Row 2 were all about the journey. Saints Row: The Third and Saints Row IV skip large portions of the journey.
- Saints Row doesn't explain backstory, but it's a very different thing: you're a nobody, and what you've been up to before considering the services of a prostitute at the wrong time and wrong place do not matter at all to the plot of the game. We are shown exactly why you are in the situation you are in.
- What you've been up to, and why, before Saints Row 2 is explained very neatly.
- What you've been up to, and why, before Saints Row: The Third and Saints Row IV are essential to the plot, and poorly explained.
I'm not saying handwaving several years in story telling is a bad thing. I love Star Wars (Orig Trig), and that has years between each instalment. "Several years pass, and now they're on an ice planet" is fine: the theme, goals, feeling, and motivations of the character remain consistent.
I'm saying that handwaving "Several years pass and now they're sellouts robbing a bank for poorly explained reasons" and "Several years pass and now they're the government despite how unlikely that is" massively changes the tone and feeling of the series: making them poor sequels.
But this is just one of the many reasons.
Of course, the changes between Saints Row 2 and Saints Row: The Third wasn't quite as disappointing as the change between GTA:SA and GTAIV, or the disappointment of Bioshock after System Shock 2. If I could find a game more like Saints Row 2 than Saints Row: The Third, then I'd love to play it.