If we really want to maximise the drying rate, we need to get the water out far more than we need to worry what angle it should hang at. This is particularly important if the towel is doubled over, as large towels invariably are.
If it is hung outside, wind direction is important, especially if we have the ability to keep the towel aligned correctly to the breeze for as long as possible.
Like most physics problems, it's much more subtle than it first appears.
It depends on how much water the towel contains.
Determine how much water is squeezed out of the towel, if it is still say 50 percent wet, and you don't have the means or strength to reduce this percentage, then hang it to maximise water seepage first. This is vital to the operation.
If you are thinking ahead, you will have drained as much water possible out first, getting it down to 20 percent is good, then hang it in a position to maximise breeze assisted / radiator drying.
So... when do you hang it widthwise, and when lengthwise
It's the amount of water you get out of it before hanging that is important,
You say what factors are important, but you don't apply them to the situation and arrive at a conclusion. Which direction maximizes seepage? Which direction maximizes breeze-assisted drying?
Sammy raises an important point, we also need to look at how the towel fibres are aligned for maximum drainage rate.
I would also conclude that, as Sammy has kindly pointed out, I should confirm that once the mechanical release of water has been achieved, in my opinion it does not make a significant difference which orientation we choose to facilitate breeze or radiator drying.
The only exception I would make to that is in the case of heavy towels with a definite pattern or fibre structure which may help as channels to remove as much water as possible.