Some have two barrel adjusters, but some have a wing on one side, and a barrel on the other side.

Does the barrel and wing offer the same level of adjustability? Will they both work for all shifters?

I think that for those with a wing, the wing is usually on the rear derailleur cable. And I guess that cable can usually be adjusted on the derailleur. But I don't know if that has anything to do with it.

Jared

That's a good question. I've got them on my Trek 5900. I thought that the swingarm adjuster was on the front derailleur, but then I usually goofyfoot my cables so that they cross underneath the downtube (helps with the cable housing curvature and length). My guess is it makes it easy to throw on the fly if you need a little trim. Could mostly be just a marketing idea, like the seat tube fin on the same bike.

the one on the right is fancier, they thought people wanted to bugger up
their STI rear adjustments while they were riding,
so the lever lets you do that, ... for better or worse.

Thats for old road bikes, modern bikes doesn't need that design just in case somebody doesn't know. You can put mix those ones with inline cable adjusters too, all depends of your taste or what do you want to do. Besides that there is no difference in functionality between the two pictured.

The stops with a thimble on both sides came with Shimano's lower line groups while the "wing" type for the rear derailleur was provided with higher line groups. Why? I have no idea.

From a practical standpoint, the front derailleur has no built in adjuster so a fully adjustable cable stop is a real necessity. The rear derailleur has it's own adjuster so the cable stop can have fewer and wider adjustments.