ITCZ, here's a shocker:
after many years with most different autopilots, I'm now flying the 777....never had an overshoot on other types, but we had one on the 777 recently. Everything correctly armed, etc, and a/c being closely monitored by all as we were in an expedited descent at near Vmo, speed brakes extended, and very fwd c.g. The a/c initially seemed to be levelling normally, and then at selected altitude, not yet in capture, speed brakes being retracted, the a/c pitched down abruptly to 300 feet below, before manual disconnect and recovery. The handling pilot said the a/c seemed to be massively out of target-speed (trim) when he disconnected. The only thing I can compare it to is a "load limit" type scenario on some other autopilots (it was in v/s, selected speed for level flt 250 knots in the window, which you'd expect it to reduce to after alt capture). Blind sided the lot of us....never expected anything like that on the 777; no harm done, but report filed, AP written up, etc.
It may be that the 777 cannot cope with 3000 fpm-plus v/s level-off at vmo, fwd c.g., changing wind and speedbrake configuration change all at the same time....it doesn't come up very often, and it's not recommended for pax comfort!! But if you're doing an emergency descent-type scenario (we'd just had a major medical emergency and were racing for the deck ) - watch out.
BTW, agree with the TCAS comments above - I try to reduce the vertical rate substantially before the last little bit, especially when passing under the arrival routes/opposite direction traffic. It's seems polite to me....