As I understand it, it's computationally faster and the same key size confers much more security than RSA. That said, there are some elliptic curve skeptics out there that think the NSA has cooked certain curves or may have techniques we don't know about and that's why they've been pushing it so hard. The latter being less likely than the former. Don't use the NIST curves.

RSA getting weaker

ECDSA suspected backdoored by NSA

EdDSA/Ed25519 like ECDSA but community made

RSA32768 might be okay but weird

ECDSA isn't thought to be backdoored so much as designed on purpose to be very difficult to get right / very easy to get catastrophically wrong.