For more screenshot comparison, you can check out the gallery (courtesy of Reddit) below that compares the pre-patch and post-patch version for Fallout 4 on the PS4 Pro. The improvements are mostly noticeable outside thanks to the improved draw distance along with the foliage density. The visuals also look sharper thanks to the supersampled image quality. Overall, it is a nice improvement over the base PS4 version.
For those asking for how much graphical improvement have been made to the game, take a look a the side by side comparison screenshots of Fallout 4: Pre vs Post-Patch (posted below). You will notice improvements mostly in the outside area. The game looks much better on PlayStation 4 Pro now.
Fallout 4 takes place in the year 2287, ten years after the events of Fallout 3 and 210 years after a Resource War over natural resources that ended in a nuclear holocaust in 2077. Fallout 4’s story begins on the day the bombs dropped: October 23, 2077. The player’s character (voiced by either Brian T. Delaney or Courtenay Taylor) takes shelter in Vault 111, emerging exactly 210 years later, on October 23, 2287.
The comparison screenshots below are in the sequence of BEFORE vs AFTER