Usually just the "Mod" version is enough as those are the newer ones, but there may be a few games that don't work with the mod version.
So just have the mod version enabled, and use the others if for some reason you wanna play a specific game that doesn't work with the mod versions.
I haven't played the entire PSP library, and nowadays I am using Adrenaline and Ark standalone in my Vita since my only reason to keep using my PSP, making the PSP DLC work, can be done in standalone Ark.
So I am sorry I can't give you any examples of games that don't work with the mod versions.