My favorite executive summary of the crypto elliptic curves is this:

     CURVE      SECURITY  RECOMMENDED BY
     ---------- --------- --------------------------------
     SECP256R1  128       IANA, NIST, FRANCE, GERMANY
     SECP384R1  192       IANA, NIST, FRANCE, GERMANY, NSA
     X25519     128       IANA
     X448       224       IANA
     SECP256K1  128       BITCOIN
     BP384R1              GERMANY
     SECP521R1            FRANCE
     GC512A               RUSSIA
     SM2                  CHINA

> Most cryptography libraries offer optimized assembly implementations of NIST P-256, which makes it less likely that your signing operations will leak timing information or become a significant performance bottleneck.

Having implemented the nist curves in assembly myself before, I must say it always amused me, how a language even more memory unsafe than C, can actually make crypto implementations stronger.