STDisjoint() = not STIntersects()?
Mathematically, disjoint = not intersects.

As to which is faster, according to the documentation on spatial indexes at http://msdn.microsoft.com/en-us/library/bb895265.aspx#methods , a spatial index can be used for a query containing geometry1.STIntersects(geometry2) = 1. 

Strangely enough, geometry1.STDisjoint(geometry2) = 0 is not listed.