I'm using a 7D and a 70D which have different max burst speeds. I want to put one on a remote for basketball. If I hold down my shutter button on, say, my 7D (8 FPS) will I get the full speed on my 70D (7 FPS) or will it only take a picture when the 70D is ready for another shot and the 7D happens to take a shot at the same time? Or, if it was reversed, would the 7D shoot at it's full 8 FPS or would it shoot only at the 70D's 7 FPS?
It depends on the capabilities of the transmitter and receiver and how the transmitter is triggered. In general if the transmitter is attached to the hot shoe or PC connection of the camera you are operating ('master'), then one short signal to fire will be emitted each time the 'master' camera's shutter fires, since that is what activates the hot shoe/PC connector. In this scenario if you use the slightly slower frame rate camera as the 'master' camera, the 'slave' camera should fire at the same rate. If the faster frame rate camera is used as the 'master', then the 'slave' will only fire when it is ready to take another shot and the 'master' camera fires. (I have read anecdotal accounts that similar triggers activate the shutter for long enough that two exposures are captured when the camera is set to burst mode.)
One way to fire both cameras continuously at their maximum rates would be to use a receiver on both cameras and fire both shutters using the button on the transmitter. Since the transmitter communicates the state of the shutter button position as long as it is held down, if each camera were set in continuous shooting mode they would each shoot bursts at the maximum frame rate for the camera, settings, and conditions as long as the button on the transmitter is held down.
Keep in mind that certain in-camera settings can affect maximum burst speed. Things like high ISO, Peripheral Illumination correction, stronger Noise Reduction, Highlight Tone Priority, etc. will all decrease the maximum frame rate of a particular camera. So will the maximum write speed of the memory card. It would be rare to get rated frame rates from either camera in a typically poorly lit gym where the ISO needs to be cranked up a little.