P-256 and P-384 are widely supported in various TLS libraries (SChannel, SecureTransport, OpenSSL, NSS), whereas Curve25519 doesn’t yet seem present in Microsoft or Apple’s libraries. I suppose with TLS 1.3 support perhaps we may see it implemented?
Unfortunately it seems none of the NIST curves (P-*) are considered “safe” by DJB and Tanja Lange: https://safecurves.cr.yp.to/.
The P-curves are "unsafe" (according to that rubric) in the sense that there are several ways to make mistakes writing curve libraries with them; you have to be more careful using them than you do with Curve25519.
Brian Smith has argued for supporting only P-256, P-384 and Curve25519: https://briansmith.org/GFp-0. That said, Mozilla decided to continue to advertize support for P-521 for NSS (https://bugzilla.mozilla.org/show_bug.cgi?id=1128792).
P-256 and P-384 are widely supported in various TLS libraries (SChannel, SecureTransport, OpenSSL, NSS), whereas Curve25519 doesn’t yet seem present in Microsoft or Apple’s libraries. I suppose with TLS 1.3 support perhaps we may see it implemented?
Unfortunately it seems none of the NIST curves (P-*) are considered “safe” by DJB and Tanja Lange: https://safecurves.cr.yp.to/.