OP_CHECKSIGADD's opcode looks like this:
OP_CHECKSIGADD <combined public key> <n> <signature>While OP_CHECKMULTISIG and OP_CHECKMULTISIGVERIFY opcodes take this format:
<nsig> <sig1> <sig2> ... <npubkey> <pubkey1> <pubkey2> ... <dummy OP_0 value>In segwit transactions, it appears that the public keys aren't even included in the redeem script for CHECKMULTISIG* (They're in the witness data, so disregard that). The size of the witness data, hash preimage and as a result the signed transaction is bloated as a result as the number of cosigners increases.
In contrast, OP_CHECKSIGADD only expects a 64 or 65 byte signature and 32 byte public key, so there is a massive space saving here over multisig transactions when several public keys are involved.