VKDoom is always based on the latest version of GZDoom since its keeps up with upstream code. I wouldn't really say it increases FPS and might even decrease it more if you turn on its extra features. The only time something might not run on VKDoom that does run in GZDoom is if the game/mod author is using a custom build of GZDoom of their own. VKDoom definitely doesn't help with mods that are CPU limited, which is where most of the lag of a lot of mods comes from.
VKDoom has optimisations in it for Vulcan which are not available in the base GZDoom. The plan is to eventually roll those optimisations over into GZDoom as well, but VKDoom can perform noticeably better on certain systems at the moment. Take for example the WAD "Escape Pod". My current setup is 64GB 3333MHz RAM, an RTX 4070 Super and an i7-8700k overclocked to 4.8GHz. On base GZDoom at 4K in the opening areas of the map I average about 50fps. With VKDoom it hits and mostly stays at my 4K monitor's VSynced cap of 60Hz/60fps.