Power Attacks themselves are quite interesting. They essentially boost your expected results from 50% (3 on average) to 75% (4.5). Whether this is a good idea vs attacking twice depends a lot on your specific tree and your opponent's ARM stat and fatigue level and whether you're spending favor.
Generally a power attacks are worth it. Only about a third of the models don't double their damage between the 2nd and 4th branches of the tree and against armor its better to give them 2 extra health instead of 4. Not surprisingly, its mostly the mounts that do best with a standard roll with their free attacks after the rider and on wild.
To that point, RRG's done a good job matching up abilities and trees. For example, Urien's damage spikes later in his tree, making him an attractive power attacker before taking Hot Blooded into account (and to make that shinier, Favor dice are better rerolls
). On the flip side, Hagal spikes early and gets a lot out of multiple attacks.
Exhausted targets are probably worth attacking multiple times instead. The free success largely negates ARM and is just gravy otherwise. If nothing else, the extra pushes are obviously an additional bonus that's very dangerous.