Trail runners are probably better for trails. However, if you’re off trail, the boots are better. Boots work better for brush, stream crossings, scree, snow, talus, rock climbing, etc.
I didn’t set out to do a head-to-head comparison, but that’s what I ended up doing in 2010. I climbed the Mountaineers’ Route in trail runners, didn’t like them, and then climbed it again the same day wearing boots. In a direct comparison, the boots won, hands down.