  We describe a finite fields magnetic gradiometer using an intense pulsed
laser to polarize a $^{87}$Rb atomic ensemble and a compact VCSEL probe laser
to detect paramagnetic Faraday rotation in a single multipass cell. We report
differential magnetic sensitivity of $14$ fT/Hz$^{1/2}$ over a broad dynamic
range including Earth's field magnitude and common-mode rejection ratio higher
than $10^4$. We also observe a nearly quantum-noise-limited behaviour of the
gradiometer, by comparing the experimental standard deviation of the estimated
frequency difference against the Cram\'{e}r-Rao lower bound in the presence of
white photon shot-noise, atomic spin noise and atomic diffusion.
