I think a combo of aerobic and anaerobic exercise/activity is probably generally best for most health wise.
I actually like jogging, though lately i don't do it often or far enough. For me, it's very meditative, i sort of lose a concrete/very sharply defined sense of self, and that's a feeling/space i actually kind of enjoy.
Extreme running (marathon etc type) may be hard on the body in some ways. Don't know for sure though.
Here is how i know running helps backpacking. I use to hike with my best friend somewhat regularly. Back in the day, i was working hard manual labor jobs like loading trucks at Fed ex, etc. But more importantly i think, and for longer and more consistently, i was regularly jogging every other day (no great distances though). My diet was slightly better than my friends too.
I could usually leave him in the dust hiking back in the day. He was on average more sedentary.
Fast forward, we don't hike together that often anymore since i moved from MA to VA and he still lives in MA. We planned the great White Mountain N.H. adventure last year. I had stopped jogging regularly, but walked everyday, plus did some other stuff with the occasional backpacking/hiking.
My friend, started jogging a couple of months or so before the trip , including some hills stuff (and has been doing yoga for a little longer).
My diet at this point is MUCH healthier than his (though his has definitely improved since the old days). However, he kicked my butt hiking, it was the reverse of the old days and i expect it was because he had started jogging a couple of months or so before hand. Granted, we were carrying similar amount of weight (both too much, which sort of led me here), and he is 3 to 3.5 inches taller, plus heavier than me, so that didn't help but then again i'm unusually strong for my size and always have been since little (and without working at it).