OK, I got the Mil-C-5040 cord in yesterday and today I did as I promised. Here is a side-by-side comparison of the two. My opinion is the commercial cord, while noticeably different is still a bargain at the price. I paid $36 per 1000 feet of commercial cord vs. $95 for 1000 feet of true Mil-Spec cord. I will use both always.
The first thing that jumped out at me was the size of the cord on the spool.

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Compare the commercial cord (black) on the right with the Mil-C-5040 cord in the middle. Ignore the commercial cord on the left as I have pulled some off the spool already. The two spools on the right are brand new. The Mil-C-5040 cord has significantly more bulk.
Next I did a side-by-side of the cord with the cores exposed. Here you see the size of the Mil-C-5040 cord (center) is a bit larger than the commercial cord and this is more noticeable when you hold it, between your fingers the Mil-C-5040 cord feels thicker for sure.

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Notice the individual core strands, they feel significantly thicker in the Mil-C-5040 cord when held between your fingers. I am not sure how much of this has to do with the physical size of the cord vs. the fact that one is 2-ply and the other a tighter wrapped 3-ply.

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I also tied a knot with each type and pulled them equally as tight to show the difference again in the bulk of the cord.

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The Mil-C-5040 cord on top is again noticeably larger.
All told, they are very similar in how they feel, it is just the Mil-C-5040 cord is IMO going to be stronger based on my perceptions. They both feel to be made of quality materials that are nearly identical. I have seen some comparisons online where testing shows the commercial cord having a breaking strength of 650lbs. and the Mil-C-5040 cord 750lbs., which bears out with the evidence here. I have no facility to actually test this stuff, but I feel comfortable that these are both quality cord that meet the spec for "550" cord.
Again, I will continue to buy both for my purposes. The cord sold at Campingsurvival.com is a bargain, most of the other sites I have found on the net are selling the same or worse for much higher cost.
After all the work I have done I would recommend you buy your commercial cord at
Campingsurvival.com for $36 per 1000' and for the true Mil-C-5040 cord I would go to
BestGlide.com for $95 per 1000'. Smaller amounts are available from both dealers.
I think this may be the definitive comparison of Commercial vs. Mil-C-5040 cord, but it is not even beginning to touch on all the cheap knock-offs to be found on the market. I have seen dozens of cheap lookalikes that would not hold up to the two I discuss here. Caveat Emptor.
ETA:
I have seen a lot of nonsense regarding the specifications of Mil-C-5040 and the number of core strands. I read the document entirely and Type III 550 cord for military use must have between 7-9 core strands and they must be 3-ply each. It also says the cord MUST have one or more unique colored threads in one of the cores to identify the manufacturer. The version of the document I have is MIL-C-5040H, which is the most recent as of this writing.