It's not a solution to battery problems. Just like any other app, it's subject to how well designed and implemented it is. Facebook, unfortunately, is not famous for having optimized apps and, as we've learned recently, it even intentionally adds bugs and quirks to random users to evaluate the impact of those and how long it takes for an user to give up on the app and use the mobile web version. And WP aren't an exception...they just don't get the same update cycles and attention given the low adoption rate (which is improving thanks to W10, but still).
In my case, Facebook neither slows down my device nor impacts my battery any more than if I used it on Chrome. If I spend 10 minutes a day with FB, it uses less battery than if I spend 5 hours a day, obviously. Enabled or disabled on my Note 5, it really doesn't make a difference. It's not without its bugs, of course, even more because I'm on the beta program, but I do miss the system integration (share, direct access to Gallery, etc.) when I try to use just the mobile version.