assuming "old school webview app" means something built with cordova (or similar), you no longer have the ability to drop down into Obj-C / Java for extensions/functionality that the web doesn't have or safari doesn't support.
In many cases this doesn't really matter, but could very easily be a complete dealbreaker for someone trying to decide what to build.
Ya pretty much meant cordova. And just for fun lets throw react native into the comparison mix. Now have 5 levels deep of options on the Web App <--> Native scale, all 5 of them still relevant in 2 years?
I've been doing React professionally for 3 years now. I've messed with React Native out of curiosity and to see if it would fit my needs.
React Native remains a hard sell for me. The idea behind it is that knowledge of React is where the learning curve is. Which is a flawed premise. React, itself, is dead simple. But ditching years of CSS and DOM knowledge and learning the React Native component API and quirks regarding iOS and Android? That's a massive hill to climb. Even with JavaScript by your side. I'd rather try Cordova+React if I had to. And if I truly wanted native performance, then it's Obj-C for me. Might as well suck it up and do it right in the first place.
I've found the transition to the native components to be the easiest part. Really feels no different than using components just like you would on the web. Hard part is that the documentation for everything has tons of missing pieces and the error messages suck.
In many cases this doesn't really matter, but could very easily be a complete dealbreaker for someone trying to decide what to build.