@tagomago Hmm, I don't have experience with iOS, but I've heard about notification issues there somewhere iirc. That's a shame :/
I don't really think 4.0/5.0 is _that_ bad, I guess you can try it out yourself first for a while (joining some public rooms) and test if everything works out?
If enabled by the user (and homeserver) Matrix uses Apple's push system to notify the app to fetch new messages. And I think the devs used Riot on iOS too, but I'm not sure.
@tagomago I don't have any problem with Matrix, at least when not using matrix.org as my homeserver.