I'm going to argue for Big Pecks
Big Pecks:The main thing Mandibuzz has going for it is its defences, as it has poor offensive stats. It has impressive base stats of 110 hp, 105 defense, and 95 special defense. In additional, stat lowering moves are somewhat common in-game, so its nice that Mandibuzz's great defense can not be lowered.
Overcoat:Overcoat is also a decent ability, and actually has some uses, but damaging weather is rather uncommon in-game, as few trainers use it in battle, and it will typically only be seen in specific locations, such as the Desert Resort or Iccurius City. However, if your Mandibuzz has Overcoat, don't feel like you have to get rid of it. Its still decent.
Weak Armor: Remember how I said Mandibuzz should be used as a defensively oriented Pokemon? While weak armor lowers defense and boosts speed with every physical hit. Ouch. Mandibuzz not only relies on its defense for success, but it does not really have use for a speed boost.
So, basically, Big Pecks is in my opinion the best ability for Mandibuzz, but overcoat may also be used if you desire. Hope this helps