Our operations manual specifically states:
"15 degrees between same direction, outbound aircraft ......."
and
"15 degrees between opposite direction aircraft provided they will pass at a point more than 15 miles from the facility"
I would never use this when A/C are on opposite sides of the VOR, when they are on the same side (still nose 2 nose) and established on radials that differ by at least 15 degrees, and will pass each other more than 15 miles from the VOR, then no problem. Some states publish a lat sep table with more radials and less distances, like 24R and 8NM as previously mentioned by someone else on here.
If they were on opposite sides of the navaid I would give the A/C in level flight a precautionary hold (paper / pretend) at the fix, then push the other A/C up or down as required achieving vertical sep prior the front end of the holding airspace plus an additional 3nm (NZ requirement if memory serves correct for opposite direction)