The IS system on your new lens is at least one stop better then the system on your old lens. Also, what camera are you using these lenses with? You should be aware that if you're using a camera with a sensor that's smaller than full frame, you need to multiply the 1/focal length rule by the crop factor to estimate the handholding shutter speed.
FWIW, the IS on the 70-200 II is excellent. The shot below was handheld (free, no bracing) at 95mm with a 0.5 second exposure.
EOS 5D Mark II, EF 70-200mm f/2.8L
IS II USM @ 95mm, 1/2 s, f/5.6, ISO 100