There is something unique about *real* hardware that even the best emulation never seems to quite live up to 100%. WinUAE is awesome, it works really, really well all things considered, but it still feels just a bit "off" at times.
There are other advantages to the Minimig and similar modern clones. One is power consumption, IIRC the Minimig draws about 4 Watts, compared to 150-300W for a modern desktop PC. It's compact, silent, and can output 15 kHz RGB for a really authentic experience. Not only that, it's effectively a reasonably well equipped FPGA dev board, having a fairly roomy 400K gate Spartan3, 2MB of fast SRAM, VGA, stereo delta-sigma DAC for audio, and a bunch of IO. It's possible to implement a number of other retro computers on the same hardware, as well as some classic arcade games.
It's not for everybody, but it's darn cool. My only gripes (from the standpoint of building my own from scratch) is that the board layout uses a really odd SD card socket that I ended up having to order from Farnell in the UK since I couldn't find anything else with the same pad arrangement. It's an amazingly cool feeling to build an entire computer from a bare PCB and see it actually work.
