It is [1]. Quantum computers, using Shor's algorithm, polynomially break any specialization of the abelian hidden subgroup problem; see [2] for a fairly complete list.
Whatever reason to prefer elliptic curves over integer factorization or discrete log-based schemes must be classical.
There's a bunch of them. There's no known quantum algorithm for quickly decoding binary linear codes, so McEliece is one. The Clostest Vector Problem in linear algebra is another trapdoor that may be QC-resistent.
You didn't ask, but it's worth saying: block ciphers, stream ciphers and hash functions aren't thought to be fundamentally threatened by QC the way IFP and DLP number theoretic cryptosystems are.
Whatever reason to prefer elliptic curves over integer factorization or discrete log-based schemes must be classical.
[1] http://arxiv.org/abs/quantph/0301141
[2] http://pqcrypto.org/quantum.html