I've always had a bit of a queasy feeling about ECC, particularly secp256k1 and ECDSA due to the Bitcoin value attracting attackers, but the whole family as well. The massive BTC processing farms are also, essentially, ECC brute forcing tools-for-hire if you know the right people to ask.

The relative simplicity / ease of understanding RSA and the longevity of it in the field, being attacked by so many academics over the decades, is what puts me at ease about its security. Shor's algorithm may take it down some day, if the issues around scaling up quantum computers are ever solved, but those issues may be rooted in the things that keep RSA secure - kind of a "conservation of effort" effect. Or not, the future is notoriously difficult to predict.