For example, if you ran the same program on the 'ibmqx2' and 'ibmqx4' computers, how much variance would there be between the results from both systems? There is the inherent presence of noise in each quantum computer, but this deals with the variance in results in a single computer. How can we compare the differences between each computer, if there is any variation?
This page might give some useful information in regards to your question:
On this page you can see the Average Measurements for $T_1$ and $T_2$ times, Gate Error, Frequency, and Readout Error for each machine since its most recent calibration. If look at these measurements for "ibmqx4" (IBM Q 5 Tenerife) and "ibmqx2" (IBM Q 5 Yorktown) you can see that the measurements differ. If you were to run the same program on both devices, there could be some variance in results based on these differing measurements, as well as the inherent noise you had mentioned.
As for exactly how much variance there would be, that is hard to say.