I agree with BillJ, a "cold war" would be the most suitable term. The federation was never at a continual state of war with the Borg. Borg incursions were few and far between and usually resulted in one ship being dispatched to one area. Lets look at the Borg incursions
FC 2063: Borg travels back in time and fires up Bozeman, Montana. The Borg ship is swiftly destroyed and the Ent-E crew later succeed in preventing the Borg from damaging history and assimilating Earth.
Regeneration 2150's: Borg left over from the "first contact" incident awaken and acquire a ship, along with some new additions to their collective. They send a message to Borg space (which may or may not have reached them) and are promptly destroyed by the Enterprise.
TBOBW 2360's: The Borg send a ship to the Alpha Quadrant, destroy several outposts and assimilate Picard. They then destroy an entire armada of starfleet ships before being stopped just as they reach Earth
FC 2370's: Borg sends a ship to Earth, a fleet of ships along with the Ent-E destroy the Cube and the Ent-E follows the Sphere through a temporal rift to stop it.
Those are the only instances of direct assaults on starfleet and its territories. War isn't really a suitable word to use in this context. We can gather that the Borg were intrigued with the Alpha Quadrant and would plan methods to conquer it, but it never seemed as if it was a priority for them (otherwise they would have sent entire fleets of Cubes). In the federation's case, it was planning for a potential war with the Borg, but due to the threats from the Dominion, these plans were quickly put on hold.