All my banks have good apps on par with the fintech startup apps I use (and actually I trust them more because they aren't moving fast and breaking things).
Same for me too - my incumbent bank's app is mostly comparable with the latest hot fintech's. The latter has nothing but a slightly more polished visual look, and that's not enough for me to trust them with my paycheck.
I use a regional bank and their app is only usable for minor day to day things. For that it's fine. But I can't do anything "serious" in it: checking account transactions are limited to only the last 2 weeks; I can't search transactions for a specific amount or merchant or date; I can't view past payments I've made for bills, etc.
For any of the above, I have to use the desktop site. These are not technical limitations either and should all be in the app if we want full parity with mobile.