Of course, classic hardware and emulation are great. But they are quite a few reasons why an FPGA/Minimig/MiST may give a better experience than emulation (or at least, makes sense)
- latency : I never had a satisfying experience under emulation as far as input delay is concerned. When I play shmups I really need no latency at all otherwise the gameplay balance is ruined... Why bother playing a game when your skills are hindered by the emulation latency !
- no underlying OS : it makes a HUGE difference. You really have the feeling you are making use of the capacities of the original machine even if it's just hardware emulation. You cannot "cheat" and cannot be distracted. We all have the feeling we have trouble focusing on a single task with multitasking, high speed internet etc. Well, with an FPGA Amiga, you can't. And it's great IMHO

Like reading a great booking instead of reading thousands of articles introductions and not remembering anything.
- rendering : although it's probably possible to have a great rendering under emulation with pixel shaders etc., it's difficult to have a perfect 50 Hz display, and a clear picture (neither blocky nor blurry). I'm sure there are some Windows and WinUAE specialists that will teach me wrong. But as far as I'm concerned, I was never satisfied, probably due to my GPU / screen / OS combination. With the MiST (provided the screen is supported) you get 50 Hz, and with subtle scanlines, for some reason, the picture looks less blocky and less blurry than what one usually gets under emulation.
As for the classic HW versus FPGA recreation, the comparison in a post below is relevant. I would just add : - very satisfying rendering with LCD screens when used with the optional scanlines (clearly better than a classic Amiga with a scandoubler on an LCD screen).
Of course... All those points are moot if compatibility is not high enough !!!