Are these two ways of doing equivalent?
Basically, its equivalent, because both the downsampling process and the differencing process are linear. (If you still want peace of mind, try doing it manually both ways with a few made-up sample values.) But if there are other oddities in your system not mentioned--especially non-linear effects--then it's not so simple. For example, if the samples aren't synchronized between the two signals then the answer is more complex.