Which do you think is going to happen first: progress against RSA that plausibly threatens 2048 (or 3072) bit keys, or progress against ECC that plausibly threatens Curve25519?
ECC is used with smaller bit lengths which makes it easier to get a sufficient quantum computer.
Of course I may have a fundamental misunderstanding here, and if so, I'd love to be enlightened.
Shor threatens RSA and ECC. Neither RSA nor ECC are considered post-quantum schemes. If quantum computing is really your threat model, you want to be doing what Google did: run both a pre-quantum and a post-quantum key exchange and mix the results with a KDF.
Which post-quantum approach you choose, I don't care. (I'm a quantum computing skeptic).
What you do not want to do is build a cryptosystem using solely a post-quantum key exchange algorithm, or, even worse, try to build a cryptosystem without any asymmetric key exchange at all. In both cases, implementation errors --- some of which, in the latter case, are probably inevitable --- will doom your system immediately.
I feel like the idea that you'd use ECC out of concern for advances in factoring or conventional discrete log isn't my own, but I'm not careful enough with this stuff to know the best thing to cite.
As always, I comment on crypto stuff principally to see if I can goad you into correcting me. :)