In my opinion, 35mm is the way to go for street photography.
I have had 11"x14" prints made from some of my 35mm Tri-X negs and they look great - very fine grain, individual hairs on a person's head rendered nice and sharp, good contrast, good detail, beautiful tonal scale, etc. I can't see why they could not be enlarged to 16"x20" size and look nearly as good as they do now.
It's all in the printing and the quality of enlarging lens and camera lens used. That along with good technique when photographing and when enlarging makes for quality prints. Also, if you are concerned about 35mm print quality at 16"x20" or larger, use an ISO 100 film such as Fuji Acros (provided you are using a film camera).
You could use a Mamiya 7II with the 65mm lens (equivalent to a 33 mm field of view in 35mm format); 6x7 negs will produce better quality prints than 35mm negs will. The one drawback to that kit for street shooting is that maximum aperture is f/4, decidedly slow for handheld street work - but an ISO 400 film will regain the exposure ground lost to the f/4 lens. You will also be changing film more often, as 120 give you 10 images on a roll and 220 will give you 20 6x7 images per roll.
Regarding print size, in my opinion print size is a secondary consideration. Some of the photographs with the most impact I've ever seen were printed at 6"x8" image size. The photographer was a Guggenheim recipient. Conversely, some of the most ordinary, mundane prints I've ever seen were made with a 20"x24" view camera and contact printed.
Making images with impact is about your photographic vision, not about print size.