The Borg would probably be one of the most serious threats in the Star Trek universe to the Empire, as has been said the Borg adaptive shielding would quickly adapt to deflect blaster and turbolaser weaponry (powerful as it is, it's still just energy, which should be able to be deflected by their advanced shielding tech once adapted), since we don't even know if blaster tech is capable of remodulation this could be a fatal flaw when any Imperial warship encounters the Borg. Another thing interesting thing is Transporter tech vs SW universe shielding, since this tech (as far as we know) doesn't exist in the SW universe who's to say that ray or particle shielding would protect against it? This could also cause problems if the Borg were to transport an invasion army over.

As far as Imperials having trouble boarding Federation vessels? I don't think that will be a problem, for one I believe Federation vesels do have air-locks, what would they do if the Transporters failed otherwise? Besides even if there were no door Imperial Stormtroopers would have no problem blasting their own one.

And indeed the comparison between AI between the universes would be an interesting one too, one with physically unsophisticated looking robotics but with highly developed almost more human than human sentient personalities. And the other with near perfect human appearance replication but with slightly less sophisticated personalities.