Among the effects predicted by the General Theory of Relativity for the orbital motion of a test particle, the post-Newtonian gravitomagnetic Lense-Thirring effect is very interesting and, up to now, there is not yet an undisputable direct experimental test of it. To date, the data analysis of the orbits of the existing geodetic LAGEOS and LAGEOS II satellites has yielded a test of the Lense-Thirring effect with a claimed accuracy of 20%-30%. According to some scientists such estimates could be optimistic. Here we wish to discuss the improvements obtainable in this measurement, in terms of reliability of the evaluation of the systematic error and reduction of its magnitude, due to the new CHAMP and GRACE Earth gravity models.