The Borg are primarily interested in technology, as stated by Q in Q Who. The reason they rejected the Kazon is because their technology sucked. But then you have the strange oddity that apparentally assimilating Earth the day before Cochrane's warp flight as considered a viable option by the Collective, despite Earth of 2063 having worse technology than the Kazon. But then, First Contact is riddled with plot holes.
If you're interested in Borg against aliens from other sci-fi shows, there's IDW's recent TNG/Doctor Who crossover Assimilation-Squared, which features the Borg teaming up with Doctor Who's Cybermen. At one point, a Borg attempts to assimilate the TARDIS.