There is ONE important distinction. If you have a tarp with a catenary cut on the tarps ridgeline, it will want the ridge line above the tarp. With those kinds of tarps, the ends curve up a bit. A continuous ridge line below such a tarp would not allow the catenary cut to function.
Other than that, I go over unless there's an expectation of snow (and that means falling from tree branches, not just the sky); in that case I go under.
The hammock structure ridge line - if you put one on - is great for glasses, night light, etc. You can use a formal "organizer" of just put loops in your ridge line and mini-S hook to them. I use a butterfly knot and it seems to take up about 5 inches of line so I factor that in when I'm cutting my ridge line length.
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