What are the benifits of using Compressed Bitcoin Addresses rather than Uncompressed addresses if same length? They are both in base58, both 34 characters long, so where exactly is the space saved? When converted to binary is there one less bit on the compressed key as opposed to the uncompressed one? (This is concering legacy addresses as I do not believe SegWit has uncompressed keys that work)
An address contains a hash of something, usually of the public key. For signature verification, a signature, the signed data and the public key is needed. Since inverting a hash is considered impossible the public key is revealed and embedded in the blockchain every time a 1... address spends an Unspent Output paid to it.
Hashes are of constant length, but the public key saved in the blockchain to spend isn't. There is no special handling code that causes uncompressed public keys to be compressed before they make it to the blockchain either. Hence uncompressed public keys take larger space and their transactions are more expensive.