tl;dr There are differences, but none which ought to have or have been shown to have a meaningful impact on health.
Relatively current research indicates that fatty acid composition varies a small amount between cows treated with rBST and those that are not (and note that this study was on produced milk, so other practices that correlate with rBST usage may actually be causal). The differences are of a few percentage points at most, and are quite unlikely to be significant factors in health. A broader look at various compounds found very little difference in practice between the composition of milk (on average) from sources that used rBST and those that did not.
Also, most of the rBST itself that made it into the milk is destroyed during pasteurization.
So the answer is tentatively "yes there are detectable differences, but not any that ought to impact health".
Note however that rBST causes health complications in cows. So you might want to avoid rBST milk because you prefer not to obtain milk from cows that are even less comfortable than normal, but it is probably not rational to avoid it for health reasons unless you habitually alter behavior to avoid even low-risk events.