Gee, where to begin?
First, the OM-1 has a much smoother shutter release than the 35SP. The shutter travel on the OM is very short, the release point is very predictable, and the shutter pressure is very light. Because the shutter release on the SP has to trap the needle and set the aperture, the travel is long and stiff. After a full day of shooting the SP my finger would be noticeably sore and tired; this never happened on any OM. The worst part about the SP is that you are never quite sure where in the long, stiff release travel the shutter will actually fire. So if you are using a slow shutter speed you can never precisely time the instant when you had to brace yourself. So, in reality, you can hand hold the OM at least a stop slower than you can with the SP (assuming the 40mm Zuiko on the OM).
As for noise and vibration, I pulled out one of my OM-1's and the 35SP to compare them side by side. The OM has no discernible vibration from the shutter/mirror. This comes as no surprise as OM's have been know for this from the beginning. There is not a significant difference in noise between the two, either. They do sound different, with the OM having a "slap", but the SP has a sharp, metallic click.
I have been using OM's for around thirty years and have run 1000+ rolls thru them. For several years I made a point on shooting only RF's to get a good sense of the difference - mainly the SP, SPn and UC but also the RC, RD and DC. In the end there was a clear choice; the OM's were the overall winner in every aspect. Especially for the 28mm FL you get the choice of three Zuikos, all of them great lenses. The best of the RF's was the "little dicky", the 35RC, due its small size and light weight.
It is a mystery as how you could possibly think you can make the OM-1 "better" than it already is, but if you really are set on a 28mm camera for street shooting, get an XA4.