The Apple TV doesn't do universal/void search for Amazon Prime Video. Not to mention it doesn't even play the content. So I think I'd rather have Netflix with text search if it means I also get Amazon content too. Plus Netflix content has been in talks about being added to universal search for awhile now so who knows, it may happen which will make that point moot.
So where are you trying to go with this? Apple TV does iTunes, Netflix, Showtime, HBO, and Hulu. Fire TV does Amazon, HBO, Showtime, Hulu, Starz, Encore, Vevo, Crackle, and Popcorn Flix. Fire TV has more services with search results right now and has Amazon included which the Apple TV does not. The Fire TV lets you use XBMC/Kodi which the Apple TV will not. The Fire TV will let you output DTS which the Apple TV will not. There are plenty of advantages that the Fire TV has over the Apple TV at this point in time but like I said before, no single box is perfect, not even a fully stacked HTPC. Also, you know what works with Amazon's universal search that doesn't work on the Apple TV? Music.
I have pretty much the same setup with a central controlled media server that works with XBMC, but none of the limitations that Plex gives me so I don't see Plex's media server being some sort of perk because it nets me almost nothing.