I switch back and forth and though I love primes (who doesn't?) I find for most things a zoom is more practical. Things like events, parties, weddings and vacation are where I prefer zooms. For me it's more about getting the shot than getting the perfect shot. Get's the job done, ready for anything sort of thing.
However, I deliberately chose all f/4 zooms so that I would still feel the need for speed (sorry that one just slipped out!)
I am getting back into the primes, I think the 135L is what did it for me. So when I'm shooting for fun or to be creative I'll use that in combo with my EOS M & 22mm. For EOS M - primes. Definitely. Wish there were more available. Currently using old FD lenses via adaptor with it.
Ideally I'd like to have all fast primes with IS built in on two FF bodies plus an assistant to carry it all! Hahaha!
Sorry, forgot to answer the Q! Do I take better pictures with primes? Perhaps but I just try and make the best of what's on the camera at the time. A prime does make you want to experiment a bit more, you always wonder - "now what if I shoot this wide open??" And then theres the bokeh! oh and of course freezing action. So I guess you have more options available.
Someone mentioned using your zoom at specific focal lengths. That's a great idea and one I need to try more of.