In my case, hobby. It's fun to tinker and play around with hardware, different Amiga models and accelerator/expansion cards, and configuring all of that within the OS. Classic gaming is also a big part of the overall fun factor.
As far as competing with the current standards and generally the technology that's available out there...Amiga is far behind and overpriced, but it's still fun to use it and play around with, if anything just for sheer kicks, no matter what.
My 2 cents. :-)
EDIT: The biggest problem with modern Amiga is the lack of software however. It lacks applications that we all require for daily use. A good example of a lacking application would be a decent web-browser.