I ride all three: multi-speed, fixed gear and single speed. The fixed gear not so much any more though for safety factors. I'm 66 and although have been riding fixed gear since I was 15 a bad accident 4 years ago convinced me to limit fixed gear riding. Before anyone thinks about saying I'm chicken for not riding it, I am riding it, just not as often.
The allure of fixed gear is definitely there and they transcend typical cycling enjoyment into a whole different level of enjoyment. At least for me they do. You lose a LOT of that with a single speed with a freewheel. Is it more enjoyable than a multi-geared bike? For me yes, sort of. Do I ride my single speed as much as my multi-geared bike? No I don't.