I've always thought it was "compare with" but "contrast to", but that's not necessarily the case.
From dictionary.reference.com/browse/compare:
Usage note
The traditional rule about which preposition to use after "compare" states that "compare" should be followed by "to" when it points out likenesses or similarities between two apparently dissimilar persons or things:
She compared his handwriting to knotted string.
"Compare" should be followed by "with", the rule says, when it points out similarities or differences between two entities of the same general class:
The critic compared the paintings in the exhibit with magazine photographs.
This rule is by no means always observed, however, even in formal speech and writing. The usual practice is to employ "to" for likenesses between members of different classes:
A language may be compared to a living organism.
But when the comparison is between members of the same category, both "to" and "with" are used:
The article compares the Chicago of today with (or to) the Chicago of the 1890s.
Following the past participle compared, either to or with is used regardless of whether differences or similarities are stressed or whether the things compared belong to the same or different classes: Compared with (or to) the streets of 18th-century London, New York's streets are models of cleanliness and order.