Energy weapon vs. Brawling Edit
Having the definite one up over Brawling due to range and AUTO (plus BURST) capability, it is greatly helpful that every character have this if they wish to successfully complete the end-game tasks. Even with Power Armor, the ability to put distance between you and the end-game enemies far outweigh the ability to land multiple hits (and more damage) on a target in most instances. Even then however, Brawling still proves an effective method of attack, even against the bots of Cochise.
In addition, range does come at a cost: limited power packs (as well as any existent cons related to ranged weaponry). However, as long as one is not wasteful of ammo, this does not exactly prose a problem.
As such, both skills are very capable of completing the game, though the latter requires much more resting due to its limited range.