Just about all Linux distros will have comparable performance.
I suggest focusing instead on which desktop environment to use. LXQt or Xfce might be worth a try, or a plain old window manager if you want to get really lightweight and can tolerate some extra work. Get a live USB image and test drive one.
(For those who don't know, most distros have a variety of DEs and WMs available in their repos. You don't have to use the one that's installed by default.)