Is one more useful in bad weather than the other?
Well straight from Wikipedia:
"A traction control system (TCS), also known as Anti-Slip Regulation (ASR), is typically (but not necessarily) a secondary function of the anti-lock braking system on production vehicles, and is designed to prevent loss of traction of the driven road wheels, and therefore maintain the control of the vehicle when excessive throttle is applied by the driver and the condition of the road surface (due to varying factors) is unable to cope with the torque applied."http://funadvice.com/r/14r4o9m05ku
"Electronic Stability Control (ESC) is a computerized technology  that improves safety through a vehicle's stability by detecting and minimizing skids. When ESC detects loss of steering control, it automatically applies the brakes to help "steer" the vehicle where the driver intends to go. Braking is automatically applied to individual wheel, such as the outer front wheel to counter oversteer or the inner rear wheel to counter understeer. Some ESC systems also reduce engine power until control is regained. ESC does not improve a vehicle's cornering performance; instead, it helps to minimize the loss of control." http://funadvice.com/r/bgffj0s31ls
So it seems the TCS has more to do with accelerating actually while the ESC is more when you are steering & breaking.
I would say the that TCS is more useful in bad weather as it tries to compensate for slipping tires. But I have never drove with either (my 1990 s10 doesn't even have anti-lock breaks :P).
honestly it depends on the driver but ESC is the car or trucks way of electronically detecting skids or slides and preventing them. TC is another safty feature to help assist in anti lock breaking
Yah I hear you there. I live in Montana - Rear wheel drive, manual with no anti-lock breaks holds your attention in the winter. You aren't going anywhere unless its a controlled slide.
I would know i live in ALASKA lots of skids and ice and idot drivers here lol