721 are non-fungible tokens, while 1155 could be fungible or non-fungible, but are mostly used for fungible game items. The advantage of 1155 is that it's much more efficient to transfer many of them, in contrast to 721, where you'd need to do multiple single transfers.
The overall advantage of standards like erc721 and erc1155 is that they're supported across the ecosystem.
RE: Day 8 of Building an Equipment System with Smart Contracts (Solidity)