Agreed with the above, I believe, your talking about the same fish,
Chiloscyllium punctatum. Maybe the Brown Banded is Chiloscyllium plagiosum, instead
?(the correct common-name is Whitespotted Bambooshark for Plagiosum)
To answer your question, they probably will get along for a bit, before becoming aggressive towards each other. Perhaps if one is male, the other is female, a pair could work. However, even with a pair, they will likely be still nippy and bitey towards each other, and the subordinate will need some space to escape to, and as I'm sure your aware, that 300gal isn't the best of homes, long term, for one of these guys, let alone 2.