I am thinking it would be a very very loooong war.
Hardly. You see, curb-stomp battles don't last long.
The borg are, BY FAR, technologically and numerically superior.
As for the dominion - they put to good use their ship building and jem'hadar growing tech in the alpha quadrant, by using the abundant natural resources on the worlds the cardassians conquered.
And yet, the federation & co managed to keep up with it, if only barely (as per Worf).
Yes, the dominion in the gamma quadrant is much larger, but still tiny by comparison to the borg.
One could say that as the gamma quadrant dominion is above the federation, so the borg is FAR above the gamma quadrant dominion.
PS - Blowing up your planets and committing suicide en masse are not conductive to maintaining an empire.