Alpine's performance mostly benefits compact programs like busybox.
Gentoo offers many distinct packages, but in fact most users follow the guide, that recommends packages for a bloated standard desktop like NetworkManager and DEs.
Most of alpine's base system and some packages are also statically linked, which is in most cases faster and than dynamic linking http://harmful.cat-v.org/software/dynamic-linking/
It links all programs against musl instead of glibc, so all binaries are generally smaller.
The musl chroot of gentoo is as well integrated as openrc for arch.
Of course the binaries cannot use any fast instructions of the local cpu, but you can still compile alpine packages with aports.