What happens if you save Sloane?

Your choice likely won't matter if a sequel is produced. I imagine between MEA and MEA2, Reyes will have successfully have taken over. Sloane will always be a bitch, and go down like a dog one way or another.

Somebody actually saves that bitch? Fuck that, I wish I could have shot her myself.

No, she shows no sign of planning to wage war against the Initiative or the angara. The only people she has in her sights is the Kett and the Collective. 
There is no change in living conditions compared to Reyes being in charge. The only difference is some ambient dialogue and the Collective are hostile towards you. 
She helps in the final mission and gives you a tsundere-type compliment. 

I wish I could kill both tbh.

Not surprised folk are needing to ask, Sloane literally gives no reason in the story to save her whatsoever. No redeemable qualities shown by her at all, the death she got offered in the end was so fitting for her character, only regret from my pathfinder was not being able to pull that trigger myself.

You mean other then not being a lying, cheating, backstabber?

It is an interesting choice. Do I choose the hard ass bitch I can trust and will do what she says she will do.

Or do I trust the overly friendly fella, who will lie to me and everyone to get exactly what he wants out of them over and over again. I know, I know.. He told me no more secrets. I soooooo believe him this time.

He at least has a good reason for not fully disclosing his true ID, and shows regret later for not doing so after you side with him. Sloane is just in it totally for herself and her own power, despite being a former security head she doesn't even pursue a twisted form of justice at Kadara, she would be happy to watch it burn as long as she still got her own piece of the pie while remaining in charge of it all. Reyes at least wants some form of order and trade going on, the choice would have been far more difficult had more shades of gray been thrown in Sloane's favour, but that didn't happen.

"I'd never stab you in the back, Shepard. Warriors like you and me - straight to the face."

I want to believe in Reyes, although the "duel" is really despicable...

Anyway, the main reason I don't want to save Sloane is because of drug business. Protection fee? I can understand. But drug? NO! This is one BIG step toward evil tyrant.

Or both. Despite my dislike of Reyes, I liked that they made him attempt this in the duel. It brings to mind that duels in the wild west were never as honorable as fiction usually portrays them.