I'm working from memory, and an incomplete understanding, so beware...
The line with the hash marks across it specifies a 'hairline'. This implies that the line will be rendered with the thinnest possible representation, regardless of the output device resolution. (Think of what happens when your LV front panel is rendered to a printer, which typically offers much higher resolution than your CRT device.) I believe the second choice (a thin line without the hash marks) will also be rendered as single-pixel width on your display, but 1/72nd of an inch (a standard printer's 'em'?), when you put real toner on real paper. (IOW, assuming you haven't specified output rescaling, a LV object that's 72 ticks in size prints out to an inch.)
Ah well. Hopefully someone from NI who REALLY understands the rendering process will chime in here.
Best regards,
Dave
David Boyd
Sr. Test Engineer
Abbott Labs
(lapsed) Certified LabVIEW Developer