Sorry about that JasonC.
In a poor but honest attempt to make amends I have done a bit of research.
That 5.6mm Battle Cord has a mass per unit length of 23.9g/m, a breaking load of 11.8kN and a cost of ?0.70/m (from a UK distributor).
I have looked up the performances of a few other items:
4mm Paracord
andrewmc's 5mm Race Rope (dyneema with a polyester cover)
Burt's Technora (not one I have come across before)
5mm Dyneema from Amazon
9mm SRT rope
6mm accessory cord.
In order to compare like with like (so far as is possible) I have modified the quoted mass/unit length, breaking load and cost/m to predict what these would be if the items were available in 5.6mm diameter.
This has been done simply by multiplying the quoted value by (5.6/diameter) squared.
The results look like this:
Battle Cord: 25.8g/m 11.8kN ?0.70/m
4mm Paracord: 15.1g/m 4.9kN ?0.59/m
5mm Race Rope: ? 12.5kN ?2.87/m
5mm Technora: 24g/m 28.7kN ?
5mm Dyneema: 16.3g/m 32.6kN ?3.47/m
9mm SRT rope: 20.5g/m 8.8kN ?0.44/m
6mm accessory cord ?(similar to SRT rope?) 7.8kN ?0.73/m
What does it mean?
I suggest the following:
The Battle Cord is indeed much stronger and denser than Paracord.
If you want strength at any price (and that will include poor shock absorbing) then Dyneema is the choice.
If pure Dyneema is available thin enough then it would be more hideable than Technora, strength for strength.
The Race Rope seems to perform poorly, but it is made of (stiff) Dyneema with a (much less stiff) polyester cover and this cover makes up a significant proportion of the bulk of the cord (it's on the outside where a given thickness contributes most to the cross-sectional area) while contributing little to the load-bearing. Presumably it's like this because Dyneema will not hold a dye and in sailing you have to be able quickly to tell one rope from another.
It should be noted that some of the information given by the suppliers (especially the diameters I think) will be approximate and any errors will be made bigger by the squaring process in the conversion to 5.6mm.
So the figures above should be taken as a guide only.
Like I said, a poor but honest attempt.