well, covers are almost always made of polyester, if you are getting say a 3mm line, the single braid will be 3mm of spectra, a 3mm covered line will have a smaller spectra core, 2.5mm maybe, the remaining thickness is heavier weaker polyester cover.
if you compare the exact same diameters, the single braid will be stronger and lighter, and almost always cheaper too, and i like them because they have a softer feel, which i think makes tying knots easier.
heck, none of it's that expensive, try both and then decide. it's always good to have extra line like that around
as for tee dee's hitch, i don't know, but i bet single braid would be fine, if you needed to, an extra half hitch would give added holding power, but may not even be necessary.