It depends on what you mean by "diameter." The rearward/tail portion of the carrier that retracts into the receiver extension/buffer tube, the AR-15 and AR-10/large-frame AR carriers are the same inside and outside diameter (the OD is roughly...don't quote me on this...0.930" on both). That's basically where the similarities in terms of size end. Obviously, because of the increased size of the AR-10 bolt as compared to the AR-15, the carrier body is significantly larger in diameter in the forward/front portion of the carrier that houses the bolt on the large-frame AR carriers.
