When Atc ask for a present heading we'd probably usually prefer the exact heading. 2 instances where I'd usually ask what heading you're flying before vectoring are when I need to put someone on a parallel track or when I want to get the idea of what the wind is doing before I start vectoring.
A couple of degrees either way in both cases probably isn't a big issue, just depending in how specific you want to be.. Especially with parallel tracking, if you're heading 142 but say heading 140 and there's another aircraft 6 miles and converging and I give them heading 140 to parallell there might still be a bit of converging.
Atc generally give headings in 5s or 0s because that is about as specific as we need to be for sequencing. It's easier to say, easier to remember for the pilots, easier to read back correctly. Only time we'd really need to be more specific is if vectoring someone around a star/Sid