As bikendan said many of the newer weight distribution hitches have sway control built in. The other alternative is a weight distribution hitch and an add on sway bar which many people have.
An equalizer is both a brand name and a generic name for a type of hitch. Kind of like many people say Xerox instead of copy. Equal-i-zer is the brand name hitch, equalizer is a generic term for a weight distribution hitch.
In my opinion you should have weight distribution with integrated sway control. I have an Equal-i-zer hitch and I like it. But it is quite heavy, greasy, and noisy in use. My friend has an Andersen hitch on his smaller trailer and I like the way it looks. It's a lot lighter and cleaner than an Equal-i-zer. If I ever get a smaller trailer I would probably try an Andersen on it.
The thing about sway control is it's kind of like insurance or seat belts. It's always there in the background, but it does nothing until that Uh Oh moment when you need it. And then you'll be glad you had it.
Andersen linkEqual-i-zer link