I've used Leica since 1952 and Nikon SLR since 1967. Leica seems much better for street photography. I could set shutter speed and aperture without looking at the camera, and even approximatly focus by feeling the position of the lens's infinity lock. Others have mentioned more advantages of the Leica for street photography. The M4 I've used since 1970 is still my favorite 35mm camera for many tasks. In that time a few Nikons and Nikkormats have come and gone. Those are obviously better where reflex viewing and long lenses are needed.
The suggestions of fixed lens 35mm cameras is valid. Some offer decent fast lenses and most are quiet. For the price of renting a Leica for a test drive, you can own an inexpensive (and expendable) camera. Do try one out before buying, though. Some may be much better or worse than others for your style of handling. Little details like the position of controls and the presence or absence of neck strap lugs can make a difference.