I don't understand how everyone thinks Baze can take more damage. Are you just looking at their stats and forgetting that once the match starts Baze has a unique that grants him 20% max health?
They have basically the same health + protection if you max them for protection, but Baze has a higher percentage of that as health, which is an advantage. Shoretrooper has about 15 more defense, which is almost negligible.
Some have posted that the auto taunt could be bad, and that the counter could be bad, but that's an odd stance. It's true, but those are both positives way more often than they are negatives.
They only reason I would run Shore over Baze is if you have an empire lead. The health gains from EP are huge, and make him worth it. But any other squad I'm using Baze assuming they are starred and geared equally.