ERC23 tokens are backwards compatible with ERC20 tokens. It means that ERC23 supports every ERC20 functions and contracts or services working with ERC20 tokens will work with ERC23 tokens correctly."

Sources: https://github.com/Dexaran/ERC23-tokens/tree/Recommended#erc23-token-standard (ERC23 and 223 are the same thing). To read the full discussion about ERC20 and ERC223, follow this link: https://github.com/ethereum/EIPs/issues/223