*Sees Cosmog's stats and movepool* I'm going to guess this is why people are saying you'll want the EXP Share on. However the end results are looking worth it...
High HP and Special Attack, good Attack, nice bulk (thoug its typing still has two quadruple weaknesses), its just the Speed that's a shame for not reaching that 100 benchmark. Though compared to other Legendaries you can do worse.
STABs with Moongeist Beam (or Shadow Ball if you don't want the low PP) & Psyshock/Psychic (it also gets Hypnosis + Dream Eater); other Special moves are Air Slash, Night Daze, Moonblast, Ice Beam/Blizzard, Thunderbolt/Thunder, and Focus Blast; if you go for mix its Physicals are Phantom Force/Shadow Claw (though no Zen Headbutt), Return, Aerial Ace/Acrobatics... you know what just stick with a Special set. Finally utilities are Cosmic Power, Hypnosis, Confuse Ray, Moonlight/Roost, Magic Coat, Wide Guard, Calm Mind, dual screens, Safeguard, Double Team, Will-O-Wisp, Thunder Wave, and Substitute.
Doesn't really have mixed potential as Solgaleo does, but it has plenty of Special options so doesn't matter. It can do what you need it to do, just the same there's no way to increase its Speed (aside paralyzing opponents with Thunder Wave). Lunala looks like it'll be much about boosting itself/nerfing opponents as it is about directly attacking (not that it can't just do that, but with its type combo it needs to be a bit more careful; luckily it has its Ability and healing).