In digital signature schemes, what the security advantage of using Elliptic Curve over Integer Factorization and Discrete Logarithm schemes?
A large advantage of EC vs RSA is a substantially shorter key (and data length due to padding). Starting to handle 4096-bit keys (512-bytes) is getting burdensome. Equivalent security of a 3072 RSA key can be achieved with a 256 bit EC key, source NIST.
If a large number of large keys are being stored there can be memory limitations and for a longer key and thus longer data this may be a communications issue.
For the same key size EC provides a higher level of security.