I've had both (a Brunton Sherpa and a bling, bling old school Thommen ) and I currently have a Suunto Altimax. The Sherpa was more accurate (both resolution wise as well as reading the correct temprature/elevation). Of course you're going to have to continuely adjust any barometric altimeter.
One thing for sure, the Suunto Altimax doesn't give you a good temperature reading when wearing the watch next to your skin (to be expected, and mentioned in the user manual). You body's heat makes it impossible to take an accurate measure of the environmental temp outside unless you take the watch off.
You can just make a lanyard for the thing and hang it around your neck like Flavor Flav (not inside your clothes. This is going to give you the most accurate temp reading. Accurate altitude measurements are a factor of how accurate your altimeter is dialed in, if the barometric pressures are changing rapidly, and the resolution of the device.