  We evaluate the sensitivity of a dual cloud atom interferometer to the
measurement of vertical gravity gradient. We study the influence of most
relevant experimental parameters on noise and long-term drifts. Results are
also applied to the case of doubly differential measurements of the
gravitational signal from local source masses. We achieve a short term
sensitivity of 3*10^(-9) g/Hz^(-1/2) to differential gravity acceleration,
limited by the quantum projection noise of the instrument. Active control of
the most critical parameters allows to reach a resolution of 5*10^(-11) g after
8000 s on the measurement of differential gravity acceleration. The long term
stability is compatible with a measurement of the gravitational constant G at
the level of 10^(-4) after an integration time of about 100 hours.
