I want to make a case for Saints Row IV: it is my go-to relaxing game. I have it installed on my PS4. The game has a GTA-esque setting and gameplay style, but where GTA is a clever satire of the real world, SR IV doesn't concern itself with the limits of reality: in fact, You play as the President of the US (with super-powers) and your main opponent is an alien overlord - with a pretty good voice actor. Now a lot of people tell me that SR III is the far better title and I bet it is, but if you haven't played the 4th installment I suggest you give it a try. It has a special feel to it that keeps me coming back. Not for the story, but for the happy accident that produced an almost meditative game. I love running through the city, killing aliens and causing all kinds of mayhem. Looking forward to hearing your thoughts on this title.
Wholeheartedly agree. It's such a fun game. Anyone who has missed it should give it some time.
That said, I have both Saints Row IV and III, and I replay III a bit more.
As was mentioned here, the overly over-the-top bits in IV sometimes make me question why I'm not just playing Lego Marvel Superheroes instead of Saints Row IV.
For anyone deciding which to get - get both. They're not overly stingy with getting through the plot on easy mode, the acting is fun, the silliness is constant, and they both go on sale regularly.
I would recommend starting with III. They're not super related, but IV does quickly spoil who in III is going to join your crew.
Edit: If I was forced to only own one of either Saints Row III or Saints Row IV, I would have to pick IV, because of the performances of legendary actor Keith David. https://saintsrow.fandom.com/wiki/Keith_David