Well, the 8371 most have been getting is the SU9400 version (1.4GHz), has 4GB RAM and has the ATi 4330 gfx.....the variant you mention above is lower spec.
Ultimately, the SU9400 (and SU7300) is a superior CPU, but maybe not enough to sway on its own.....of course, the 8371 tends to come with Vista Business, so if you need to fork out for W7 it can be a factor too. The 8371 comes with Bluetooth, also, which the 3810TZG does not, but the 3810TZG has HDMI out in place of VGA......then the 8371 has a fingerprint sensor and matte screen, the 3810TZG has no fingerprint sensor and a glossy screen.....
Have to love the construction of the 8371 also - magnesium alloy goodness - as well as the potentially valuable HDD shock protection system.
All in all, though, both machines seeem to offer a lot for the ££s