Bisharp has a better type, an ability that has a chance at raising its attack 2 stages (which, assuming I know Zygarde's moveset and programming) that may activate (5% chance each turn, I think), better stats in every stat, except Attack (and Breloom only has 5 more points in attack), immunity to Sandstorm and Poison, along with Poison and Psychic moves. I also have made considerable progress on getting a +Atk nature, high level Bisharp. I also have Defiant Bisharp, but no Technician Breloom (I don't think I even have one in any game). I also think that Bisharp is cooler.
Also, Thunder Wave is easier to teach (TM vs Move Relearner) and more accurate (100% vs 75%).