It's stille arly yet, but this has been my experience with Ancient Ones.
Yog-Sothoth: Cake. The big deal with Yog-Sothoth is just having enough Clue tokens and spell-casters, so he's pretty easy to beat. I can pretty much assure a victory against Yog-Sothoth with no problems.
Cthulu: Surprisingly easy. Cthulu is a challenge, no doubt, but fairly easy to mange so long as you have Silas.
Aazthoth: Difficult. I'm surprised he's the default choice for new games. He wouldn't be so bad if it weren't for one mystery that requires a clue expenditure while closing a gate of a particular omen symbol; pulling that off once is a good trick let alone multiple times.
Shub-Niggurath: I have still yet to win a game agaisnt SHub-Niggurath. I have tried multiple times with different combinations of investigators, and each time I come up short. Jim, Jacqueline, Lily, Lola, Leo, Silas, everyone just gets pulverized.