Blackbeard has three entities in him: Teach, Xebec, and the original enemy of Joy Boy.
His most dangerous personality is the one who uses those claws, but, he only comes out at certain times.
Blackbeard is usually shown as unskilled in raw physical combat, taking punches all over the place. Yet, he scarred Shanks with what were clearly his claws.
The fact that the normal Blackbeard fights like an opportunistic coward, but was able to use those claw weapons to injure a man, Shanks, who clashed evenly with Mihawk with swords, proves he is either hiding his full power, or has different personalities that fight differently.