GNOME Web (aka Epiphany) is the default web browser for GNOME desktop environment. Although the popularity of it is not growing significantly, it's one of my must-have browsers. The reason behind that is because it's the few WebKit based browser on Linux still maintained, comes particularly handy when testing websites.
GNOME Web is based on Apple's WebKit rendering engine. Since Apple never released the Linux version of Safari, it's safe to say that GNOME Web is the top choice for UI/UX debugging on Linux.