The closest I have ever come to drinking A&W from the tap would be a modern soda fountain, and I'm not even sure I tried it then.
I have drank pre-mixed A&W though. It isn't bad. I prefer IBC though. It's not really so much the flavor. Flavor-wise, most brand are about the same to me. I like IBC's "snap". Not really sure what you call it, that sort of almost tangy almost spicy quality. I guess that's what Barq's means by "bite." To me, IBC has the best "snap", or "bite".
It's not wise to drink a lot of it though, I think it may have given me a headache from overindulgence a time or two.
I would say Mug Root Beer is probably my least favorite. Seems very weak, almost tastes like Pepsi mixed with A&W. Not a good combo, IMO.
Jones Soda makes a pretty good root beer, IIRC. Sweetened with Cane Sugar I think. If it had as much snap as IBC, it'd be in close competition.
Barq's works well enough if you want "root beer now, dangit!" As close as you can get to IBC without being IBC.
I think A&W and IBC were once both bottled by Dr. Pepper/7-Up.