Sky Attack is a wonderful charge move for Lugia. Very quick, and unique Flying type coverage that's only seen in a usable capacity by Hurricane Dragonite. 2-bar is also very nice for defending and for sweeping gyms.
Extrasensory gains STAB and has high energy buildup. Dragon Tail, as you mentioned, has great neutral coverage, so it depends what your Lugia is going to be used for. As a counter (Machamp, etc.) or a generalist, use Extrasensory.
I use Dragon Tail on my Lugia. While this renders it less than useful for Machamp raids, it opens up the possibility for Lugia as a tanky Psychic neutral counter, particularly against Focus Blast (Lugia double resists Focus Blast, while Tyranitar is doubly vulnerable to it). It also hits Dragonite effectively while not being weak to any Dragonite moveset, a benefit only shared by double dragon Gyarados.
