I went from a 3 wire fan to a 4 wire fan. 1 black, 1 white, 1 brown and 1 brown with white stripe. I wired the 3 wires as before to the capacitor. I attached the brown/white wire to the terminal next to the brown on the capacitor. The fan turns, but slower than before. I removed the brown/white wire from the terminal and the fan speed increased significantly. Should I leave it off and cap it or what?

There must be another wire hooked to the capacitor coming from the contacter. This wire is powering the capacitor, so you can merely leave the brown/white unhooked and cap it off. Or you can unhook the wire from the contactor and hook the brown/white up there and it will do the same thing. Easiest would be to simply leave the brown/white unhooked and wire nut it. Now, all that being said, if you could post a pic of your wiring, showing capacitor and contactor, we could verify this. This should all be shown in the wiring diagram of the new motor.

Another way to wire it is: Black to one side of the contactor, White to the other, Brown to one terminal of the cap, Brown/White to the other cap terminal.