They use WebKit. So I guess roughly on par with Safari, albeit with a (significant?) delay.
A browser and its privacy is much more than the engine. You could take webkit and make the most spying browser ever out of it. Most of what Safari does for privacy resides outside the engine itself.
Although I'm not a huge Gnome fan, I don't think they are predatory like that. AFAIK it's just a then wrapper around upstream tarballs.
I didn’t mean to say Epiphany actually is invasive. Just that the engine a browser uses doesn’t tell anything about privacy at all.
Depending on that delay, it could be a significant security problem. A known (n-day) vulnerability is still very useful when software has a lag in updating there components.