Forgive my ignorance, but SHOULD the grounds be connected?
3.3V isn't an absolute value, it's 3.3V from some reference point, usually ground. If the two grounds are different, then 3.3V may be an entirely different energy level amongst the devices. Without the grounds connected it would be like trying to determine if somebody is taller than you while they are standing on a stool. If two devices are trying to communicate and are have separate power supplies, their grounds need to be connected.
The basic problem I'm having is that I need to power 2 devices with 3.3V. When I tried to connect both to the same 3.3V pin on one board, it didn't seem to work. Not sure why, but my guess is that the voltage was right but the amperage (guessing here) was wrong/insufficient. Thus the attempt with 2 boards.
You need to look up, or measure the current draw of the two devices that you are powering. You then need to make sure it's under the rated maximum of the 3.3V regulator.