I always leave the assimilated ships and kill the Borg ships that cast the regen or assim abilities, if your fleet is not big enough for this, retreat.
Akiras seem to get assimilated very easy, I don't use them fighting Borg fleets. I use Sovs and Galaxies with a pile of Novas and Intrepids to kill their fleet, some Miradas and Excelsiors for meat shields and regen, then replace losses with Akiras to kill starbases and structures.
The reason that the AI targets the Akiras is because they have the anti-module (i.e., anti-structure) roletype. The AI targets (non-cap) colonizers, siege (i.e., planet bombers), and anti-module first because they can presumably F-up their planets/defenses.
If you wanna go mano-a-mano with the borg, you need a lot of Intrepids - usually about one Intrepid per borg ship. Since you have to outnumber them anyway, this shouldn't be a problem. On top of that, healing ships like Excelsiors and Novas are clutch to preserve your fleet. I question the utility of meat shields against the borg compared to more firepower (e.g., more Intrepids), but some people have obviously had luck with it.
Also, note that Excelsiors cost a lot of money, build slowly, and die too quickly until you get the Lakota refit. If you want to integrate them into your fleet, that upgrade is clutch - otherwise, just build more Intrepids.
P.S. - As a side note, the role of the Intrepid as the Starfleet "heavy frigate" instead the Excelsior is probably the only spot in this mod where I would say it isn't quite canonical. The fact that such a minor detail is the least canonical part is a tribute to the efforts by the mod team.