What are the advantages (real or perceived) of a 2 stage trigger versus a single stage trigger on an AR-15? Thanks

The advantage is a lighter trigger pull. The disadvantage is that double taps are not as fast.

The two stage is best for precision shooting.

The first stage take up is followed by a perceptible stop, then a slight increase in pressure breaks the shot.

2 stage for precision and single stage for speed.

I'm not sure I share the same opinion as the previous posters. I have single stage JP triggers on both my AR15 and AR10, both set up with the 3 pound hammer spring. I don't see how the second stage of a two stage trigger could be better for precision shooting. But, I have to confess a lack of experience with them. I have always used single stage triggers on bolt guns, so I just did not want to get used to a different trigger action. Of course, the 3 pound spring I use would not be appropriate for tactical or military use, as some military primers are too hard for reliable ignition with it; but it has never been a problem with commercial ammo or reloads. So, I would say that a GOOD single stage trigger is probably as good as the military style, two-stage match trigger for precision shooting. But, you have to be used to it in order to have adequate control in all situations.

Like the commercial used to say - Try it, you'll like it...

The second stage is basically a 1 lb letoff, so it is in effect lighter than a 3 lb single stage.   The "surprise" break of a single stage takes significantly more pressure and can disturb you sight picture prior to the shot.  

As an example, the groups from my SPR wannabe shrank from around 1" to 0.6" when I switched to a KAC two stage.

A 2 stage trigger removes the "suprise" from the suprise break normally associated with precision shooting.  You know EXACTLY when the rifle will go off.