No speed difference. The only difference if hooked up correctly would be, the trim on the shifter would be limited, so you can't over trim the boat at speed and put added strain on the u-joints. Thr trim on the dash would be for "trailer trim", this allows the drive to go higher for trailering.
Some OBs have have 2 speeds when trimming, one for running which is slower for smaller trim increments, but once it reaches a certain height it is faster for "trailer trim".