Sturdinja is going to get a lot worse in BH due to Sunsteel Strike/Moongeist Beam. Pokemon no longer have to waste their ability on Mold Breaker to beat it, and It's almost a guarantee that they'll have a BP no less than 100, so they'll probably be useful outside of their ability bypassing effects.
One thing I've noticed so far about Sun and Moon so far is how many new abilities there are, and how many of them are fucking broken. I can see a lot more ability bans in BH and AAA.
Examples:
Dazzling - Good on both HO and Stall, makes priority a lot worse if Giratina-O becomes a trend. Not entirely sure if this would be broken or not though.
Disguise - Again, not entirely sure if this would be broken or not, but it would guarantee setup and the like. Think of Protect + Speed Boost, but with far more versatility.
Innards Out - Isn't really broken as much as it is uncompetitive, if you put it on something like Wailord then you guarantee a kill. At a price, but this is still pretty uncompetitive.
Stakeout - Dealing double damage on switch-ins is already overpowered. But "enter the field mid-battle" So basically, after you manage to kill/force out the first Pokemon on the other team then your moves deal double damage.
Wimp Out - Wimp Out Giratina-O + Deoxys-A. That is all.