Let M and N be finitely generated graded modules over a graded complete intersection R such that Ext^i_R(M, N) has finite length for all i >> 0. We show that the even and odd Hilbert polynomials, which give the lengths of Ext^i_R(M, N) for all large even i and all large odd i, have the same degree and leading coefficient whenever the highest degree of these polynomials is at least the dimension of M or N . Refinements of this result are given when R is regular in small codimensions.