In short, are
STIntersects() antipodes of each other?
According to the documentation, it seems that they are. But there is no explicit note about it.
Are there any tricks? Which one is faster, for example?
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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.
geometry1.STDisjoint(geometry2) = 0 is not listed.