  With one exception, previous analyses of the measurement accuracy of
gravitational wave experiments for comparable-mass binary systems have
neglected either spin-precession effects or subdominant harmonics and amplitude
modulations. Here we give the first explicit description of how these effects
combine to improve parameter estimation. We consider supermassive black hole
binaries as expected to be observed with the planned space-based interferometer
LISA, and study the measurement accuracy for several astrophysically
interesting parameters obtainable taking into account the full 2PN waveform for
spinning bodies, as well as spin-precession effects. We find that for binaries
with a total mass in the range 10^5 M_Sun < M < 10^7 M_Sun at a redshift of 1,
a factor ~1.5 is in general gained in accuracy, with the notable exception of
the determination of the individual masses in equal-mass systems, for which a
factor ~5 can be gained. We also find, as could be expected, that using the
full waveform helps increasing the upper mass limit for detection, which can be
as high as M = 10^8 M_Sun at a redshift of 1, as well as the redshift limit
where some information can be extracted from a system, which is roughly z = 10
for M < 10^7 M_Sun, 1.5-5 times higher than with the restricted waveform. We
computed that the full waveform allows to use supermassive black hole binaries
as standard sirens up to a redshift of z = 1.6, about 0.4 larger than what
previous studies allowed. We found that for lower unequal-mass binary systems,
the measurement accuracy is not as drastically improved as for other systems.
This suggests that for these systems, adding parameters such as eccentricity or
alternative gravity parameters could be achieved without much loss in the
accuracy.
