Your best bet would be to first pull the woofers from both speakers and then note the model numbers (of the woofers, not the speakers), which should be stamped on the back of the magnets. If they're the same, then congratulations, you're done. If not, google both models and see if you can find specs for both. If the specs are the same then you can swap them. If you're not sure then come back here with the information you've found so far.
If the speakers are the same age then it's a decent bet that the woofers are the same. But since Bose used the same model numbers through several generations of speaker, there are other variables to be concerned with as well.