Answer:

The bottom line to any aerobic benefit is the stress that you put your heart and cardiovascular system under while you work out. If your heart rate was equal during trail running and pavement, then the aerobic benefit would be pretty much equal. If you go 5 miles but the trails are hilly and the pavement is flat, then it is likely that you would work harder on the trails and your heart rate would be higher, thus eliciting more of a CV response. In addition, soft dirt, plus roots, and other obstacles, might contribute to a higher energy expenditure during trail running, and that would, in most cases, add to the total work as well. A similar example would be running on soft sand. Sand would be more work than pavement because you would sink into the sand and have to pull out of it.

There was an interesting study published recently that showed a slightly higher energy cost on a treadmill that had a soft deck compared with a firm deck because the firm deck caused more propulsion so the runner didn't have to spend as much energy lifting the legs. This would be consistent with the notion that running on soft sand would be more work than running on firm terrain.