I've been photographing since the 1960's, starting with SLRs for the most part. I then got a Nikon RF, took it to Africa in the 70's, had it stolen, and didn't get back to RFs until about 8 years ago.
I think there are two main differences, at least to my mind. When I look through an SLR, my mind is caught in the act of looking at the overall picture, as if I am looking at the picture on a wall and I'm judging how it looks as a composition. With the RF, I seem to be less concerned about framing than about the moment of pressing the shutter release and the instant that I'm capturing. I react to the image in the RF viewfinder differently.
One thing that drove me -- as if driving were necessary -- to RFs was a family event I attended several years ago with my Contax SLRs and several zoom and primes. It was an indoor wedding event at night, and I'll be damned if I could focus a wide angle image at all. I dearly regretted not having an RF that facilitated focussing, especially of wide angle lenses, and especially in the ambient darkness.
So, I usually walk around with an RF. But if I need to do close-ups or telephoto shots, it's an SLR all the way. Leica NOOKY attachments are fun, but nothing beats looking through the lens in certain situations.
FYI, I've got Leica M and LTM, Nikon, Contax, Minolta CLE and Kiev RF cameras. Each is a bit different and each has its own attributes. As does the leaf-shutter Konica IIIa, with its great lens and flash sync.