Will the Roku Streaming Stick + perform better than the original Roku Streaming Stick? My WiFi router is right next to the TV so range is not important. My TV is 1080p so 4K is not important either
Perform better in what way? Sticks have been made for years, so a newer model will seem to be more responsive than a really old model and probably have more memory for channel storage and buffering. Since your router is right next to your TV I really think you should get an Ultra and use a wired connection. You'll avoid Wi-Fi headaches, overheating issues, underpowered issues, and won't be beholden to Roku if you need a new remote.
When it comes to streaming my oldest Roku performs every bit as well as my newest, but then I don't care about 4k or any of the elaborate audio formats.