I have an older Roku stick (3500, I think). The app has a noticeable delay when displaying shows and movies. I don't think it has to do with the app. I think it has to do with the performance of the stick.
Would upgrading to the newest stick make the app faster?
Indeed your 3500 stick is under-powered compared to a newer roku box. A newer Roku such as the Premiere+ would be much better in performance with apps. However, WiFi only streamers such as your Roku stick also can play a part. I would recommend avoiding any WiFi only streamer and get a Roku with Ethernet if you can. I use my Roku Premiere+ hooked up Ethernet and have no performance issues, Everything loads fast and plays smooth and stable. Even my 80Mbit 4K UHD videos using direct play. It's flawless. None of this is possible for me using a Roku Stick. I bought the newest one and it just choked out, had to return it for a refund. Bought the Premiere+, could not be happier.