Looking at key recovery, if the public key is transmitted along the verification (while it is implicit in recover), then the difference between recovery and original scheme is in favor of the recovery version, because a public key (incompressible polynomial, 896 bytes) is replaced by the s2 field of falcon (which can be compressed to 630 bytes) and a hash (32 bytes).
Of course for the current experimentations, we don’t have the implicit, but we could imagine to have this public key hashed in the smart account storage, verified during deployment.