According to
http://pari.math.u-bordeaux.fr/dochtml/html-stable/ the function polredbest() "computes an LLL-reduced basis for the ring of integers of ℚ[X]/(T), then ..." which seems to imply that some expensive work, including factorization of the discriminant, is being done. For polredabs() this is made very explicit with warnings about how expensive it might be, but there are no sych warnings for polredbest().