In the years that I shot weddings, I shot exactly one on 35mm - the first one!
All the rest were shot on 120.
They were all shot on Kodak professional colour print film - initially on the various versions of Vericolour, and then the Portra films that replaced it.
I still have almost all the negatives. The work-flow involved in selling enlargements to my customers just wouldn't have worked with transparency materials - the labs that did good wedding work and the materials available were not set up for it.
Have you ever tried to photograph a bride in a white dress and a groom in a pale blue tuxedo? If you had, and had used transparency film, you wouldn't have tried that film again.
I realize that I might be dating myself a bit here.
The only thing I will say about the 135 vs. medium format part of your question is that all colour print film today is significantly improved when compared to, e.g. 1975, so the results from 135 might very well be closer to acceptable than they were back then.