This is a bit much to go over in a forum post. Contact a dealer, get a demo of CatDV, or check out the demos on youtube or catdvexperts.com.
There is not a lot of comparison between CatDV's server system and Bridge and FMP. It's more like a merging of those two products.
For instance, and this is about all I can go into, CatDV can automatically ingest your video footage, extract pertinent metadata (automatically) and then enter that into your database, automatically meaning that you don't have to type names, or locations, or codec or, or, or... you get it. Additionally it can handle hundreds of thousands to million assets.
CatDV is more in the range of Dalet or North Plains or Media Beacon as far as comparisons go and if you want to look at Apples vs. Apples. Price-wise, CatDV starts in the thousands of dollars for a server-based system whereas the others you mention are a few hundred at most.
Final answer, CatDV scales better than Bridge and handles media better than Filemaker but is in a different price range from both.