Is there any advantage to using larger stones in a free-standing dry stack wall?
There are two reasons for using various size stones in the wall: 1) strength, and 2) appearance. 

1) The strength of a dry-set stone wall is largely determined by the placement of the rocks within the wall.  Stone walls are stronger when the stones (rocks) “fit together” and are of various sizes. If all the stones are the same size, they tend to “roll” and act like marbles. 

If you’ve ever walked on a gravel road where the rocks are all about the same size, you’ll notice that it’s like walking on marbles. 

Yes, the larger rocks are more difficult to “slide” and excellent in a retaining wall, but they work well to stabilize a non-retaining wall too. If all the larger rocks are placed at the bottom with smaller rocks on top, the top rocks will tend to be unstable. Various size rocks will help “bind” everything together, but they need to have the correct gradation. 

We call using various size rocks “gradation”. This gradation is very important in gravel roads, concrete mixes, etc. so that the rocks bind together. 

2) If you’ve ever seen a really good mason work on a wall, you’ll notice that he’s half artist and half laborer. I don’t know how they do it, but when they’re done you’ll notice the rocks are all blended together and none of the rocks “stand-out”. That is to say, they all seem to blend together...not all the large ones are on the bottom, etc. 

I think the key to a good wall is taking the time to “fit” all the rocks together. Sometimes that means chipping the rocks so there are various sizes and various shapes that fit into those small little spaces.