Assuming you are making the most of 35mm, medium format will give you slightly more sharpness, and a little more detail, depending on the print size of course. Tonality - in my opinion the differences are trivial. The real step up in that area is to sheet film. And of course, technique, since tonality has a lot to do with printing skill. John Sexton's prints from his Hasselblad negatives look great. You might mistake them for large format. On the other hand most of the prints I've ever seen by other people using medium format look like they might as well have been made from 35mm negatives.
So I guess you can put me in the camp that doesn't see a whole lot of benefit to medium format over 35mm. I never much cared for the square negative, so I ended up doing a lot of cropping anyway. And the other types of medium format systems out there are often quite limiting in lens selection. Further, I didn't find medium format all that much less clunky than my large format gear. So I went back to 35mm when I need the convenience and use sheet film otherwise.