I’ve seen it claimed that downhill running has a negative effect on strength training outcomes, the rationale being something to do with the eccentric contractions. Is this supported by evidence? I’ve always thrived on trail runs, the hillier the better, but could be persuaded to stay on level terrain if that’s better somehow.
The only data I’ve seen on this has suggested an increase in eccentric strength and knee extension force production with downhill running compared to level ground running, though these effects have not been quantified in actual resistance training, e.g. squat or deadlift performance.
In general, I’d expect downhill running to improve adaptations specific to that task, which would mostly be involved in eccentric force production and tendon stiffness to some degree. I would imagine the carry over to powerlifting to be relatively low.