Shor's algorithm generalizes to any hidden subgroup problem for finite Abelian groups [1], which includes integer factoring and elliptic curve discrete log.
I don't believe there's a publicly-available algorithm that's faster than Shor's for breaking EC, and to clarify any misconception you can also use Shor's for EC (EC is actually easier to break with Shor's than RSA, but EC has the advantage of shorter keys for longer brute-forcing using known classical methods).