Comparison of Curve25519 with secp256k1?

Question

How does the security of Curve25519 compare with secp256k1? Is it known why the creators of CryptoNote may have chosen one curve over the other?

Answer 1

https://safecurves.cr.yp.to/ (joint work between Daniel J. Bernstein, University of Illinois at Chicago, USA, and Tanja Lange, Technische Universiteit Eindhoven, Netherlands) has rated Curve25519 as "safe"

The specific reasons why CryptoNote creators chose Curve25519 are unclear but it appears to be trusted by top cryptographers.

Monero developers trust DJB, Curve25519 and the fast Schnorr algo (EdDSA).

Riccardo Spagni has stated:

We will absolutely switch curves if sufficient evidence shows that the curves / algos we use are questionable.