I don't see how Safari would drain a battery any more than other app that goes online. Such as Facebook or Twitter. I had a battery drain issue after 8.1. I found where several new widget apps were using background app refresh. Turned those off. I then Reset Network Settings. Also turned a few apps off in location services. They were new. My battery seems to be OK now. Well, for a 14 month old iP 5.
Sent from my ancient but trustworthy iPhone 5.