This tutorial/explanation seems to contradict your question's premise(?). But the pertinent part says:
The difference is under the covers: the geography index will correctly handle queries that cover the poles or the international date-line, while the geometry one will not.
There are only a small number of native functions for the geography type:
ST_AsText(geography) returns text
ST_GeographyFromText(text) returns geography
ST_AsBinary(geography) returns bytea
ST_GeogFromWKB(bytea) returns geography
ST_AsSVG(geography) returns text
ST_AsGML(geography) returns text
ST_AsKML(geography) returns text
ST_AsGeoJson(geography) returns text
ST_Distance(geography, geography) returns double
ST_DWithin(geography, geography, float8) returns boolean
ST_Area(geography) returns double
ST_Length(geography) returns double
ST_Covers(geography, geography) returns boolean
ST_CoveredBy(geography, geography) returns boolean
ST_Intersects(geography, geography) returns boolean
ST_Buffer(geography, float8) returns geography [1]
ST_Intersection(geography, geography) returns geography [1]