As far as Peter and Miles...
I mean, for one, Miles is ostensibly not supposed to be as strong as Peter from a baseline physicality standpoint. That's why he has powers that compensate for that. I don't know if it was because Miles was 13 versus Peter being 15, but I think Bendis intended that the different spider bite gave a different level of power.
Peter's main power isn't just his Spider-Abilities but his creativity and intuitive thinking, which lets him out-think his opponents and use his powers in unexpected way. Miles to me feels more instinctual in how he acts, combined with emphasizing the Venom Blast, but he can still be creative, he just doesn't have the same kind of mindset than Peter does.
As far as the game is concerned, Miles definitely dealt with probably a bigger threat than Peter did in his initial months as Spider-Man (although who knows, maybe Kingpin almost accidentally destroyed the city once or twice) but that's also a world that's had an active Spider-Man for several years so it stands to reason crime and Supervillains would be on another level than they would've been pre-Spider-Man. And Miles' own inexperience is partially why things escalate to the extent they do, but it was his first major job as Spider-Man so there's obviously going to be some growing pains there.
This reminds me of the Marvel's Spider-Man cartoon where everyone and their mother gets Spider-Powers and seems to get a handle on them quicker than Peter did on the same show. It's like, I'm not necessarily against giving supporting characters the same powers as the protagonist, but at least make it apparent why your protagonist is valuable and not redundant (not helped at all by the fact that Peter constantly needs help or to be saved on his own show).