In my personal opinion I think that both the round and square will probably perform the same.  Or at least the more important thing than round vs. square is the thickness of the metal.  The ones that I bought are in my opinion the beafiest ones on the market.  AJ's also makes round rails that are the same thickness as well.

One performance difference that you will only see with some round rails is that some of them have the round rail pitched down or up.  So if they were pointed down you might loose SOME (very minimal) ground clearance.  Here is a link to an install of the round ones that pitch up, so just look at that second rail that is higher than the bottom of the XJ and imagine it being lower then the first bar, almost like a step.
http://www.jeep-tech-tips.com/custom-4x4-rock-rails-install.html

I think that it just comes down to prefference.  Find a width that you want to go with and then which ever you prefer, go with them.

Honestly it's really a matter of preferance and what you like best. I'm not a fan of the square side rails as I simply don't like the way that they look. However becuase I do not like them that does not mean that they are junk or that someone else won't like them.

As far as what is stronger, a round tube typically of the same wall thickness of a square tube has a higher yeild tortional (sp?) strength to it. (aka the round tube is stronger). However the side rails really don't serve for anything more than keeping the Jeep futher away from something. I guess they can be used for a step, but thats really not they were originally designed for.

So go down, some go up, and some go straight out. Once again personally preferance to what you like best. Only thing I can say is that the one's that go up may protect more of your lower rocker than the rest.

Mounting is a very important thing when it comes to rock rails. The pinch seem is VITAL on the way that they perform. As shown by the picture that Wade posted, without the pinch seam tie-in the rail when put under stress will bend upwards and damage the the rocker panel rather than protecting it. Some companies really don't do much in the fact of pinch seem tie-in's. For instance JCR only have a peice of flat bar stock welded to it, it may "help", but in my opinion does not solve the issue. Others use a peice of bar stock with threaded inserts to attach to the pinch seem. Here is a photo of my Motion MJ rails to show what I"m talking about.



The smaller bar is what I'm talking about. I just feel it's stronger to have an actual bar than it is to have a peice of thin bar stock.

Also strength will come in the wall thickness of the main bar. AJ's is 3/16" or 1/8", I know my Motion one's are almost twice as thick at 1/4". One would have to say, the thicker the sidewall thickness is, the stronger they are.

Once again just opinions and personal preferance. It really comes down to what type of wheeling you do, how your going to use your Jeep, and what amount of $$ you want to spend.