I've found that if you are using an older phone then you will certainly notice that Flutter is not as smooth as a native app. However, I know the Flutter team have made a lot of progress with performance so it may not be so bad.

Three largish apps you can try are:

1. The Alibaba app:

Alibaba app for Android → http://bit.ly/2NQJcMX Alibaba app for iOS → https://apple.co/2NjVGxf

2. The Hamilton (musical) app - search Hamilton on Play Strore or App Store

3. The inKino movie database app. The source code is available here: https://github.com/roughike/inKino