I play on both but I haven't compared them side by side. In my experience there is very little difference, with the Pro appearing to have a slightly higher frame rate. TSW 2 however won't apparently run at 1080p on the standard PS4 whereas the Pro will offer a HD or 4K option.
The frame rate doesn't appear to be locked so you are probably looking to get a slight FPS boost on the Pro.
If you enable the Pro's Boost mode (in settings) then yes, there is an improvement in frame rate and loading times. Boost mode helps for most games that don't have Pro specific settings because it unlocks the machine's restricted performance limitations. I leave it on and have never had a problem. Without boost mode on the game's performance will be similar to a "standard" PS4 - because TSW2020 isn't Pro enabled.