Richter's Holy Water has aura properties, while Simon's Holy Water has fire properties. This affects how each move interacts with certain characters' moves and items. Firstly, do not be fooled by the aura properties of Richter's Holy Water, for it does not scale with damage like Lucario's Aura mechanic would. Second, this difference is only necessary to a few characters. Richter notably does better against Olimar than Simon does because his aura Holy Water will damage Red Pikmin while Simon's will not. However, Simon's fire Holy Water will cause certain explosives, notably Link's Remote Bomb and Steve's TNT, to explode while Richter's will not. These differences are not important except in very specific scenarios--particularly when Link is holding a Remote Bomb, drops it due to taking damage from Holy Water, and the fire causes the bomb to explode--so just pick whichever Belmont you prefer.
You can read up on the differences at SSBWiki.
You can read up on the documentation that effectively covers both of these characters on Simon's character page.
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