2:33 p.m. on November 1, 2010 (EDT)
In the "all in one" wrist units, like anything else, you get what you pay for. Over the years, I have had a number of different altimeter, compasses, watches, and thermometers. And 2 of the 3 brands you mention, plus seeing the third one in use by other people.
First, I will echo Ed's (whomeworry) comment - if it has batteries, the batteries will die at a critical moment. No ifs, ands, or buts about it. So if it is mission-critical, have backups.
On the compass - electronic compasses, whether in the watch or a separate handheld electronic compass, do not begin to compete with an analog compass with a magnetized needle. Considering that you can get a compass that will serve all your needs short of surveying (and maybe competitive orienteering and telling the artillery where to lob their shells) for $10, just get a baseplate compass by Suunto or Brunton (US distributor of the Swedish Silva company). The JWA Silva (which are now made in China) are ok (originally Silva of Sweden supplied the JWA company with their compasses, but there was a trademark dispute that ended with JWA owning the US trademark rights to the Silva name). Just in case you travel to the Southern Hemisphere, you should know that because of the way the Earth's magnetic field works, you will need a Southern Hemisphere compass outside North America and Europe.
On the thermometer - the big problem with the thermometer in the wrist instruments is that it is reading the temperature on your wrist, not the free air temperature. You can get a backpacking thermometer that looks sort of like a pencil for $4-5. Get that instead, if you want reasonably accurate readings. And the "zipper-pull" thermometers are plenty good enough for most backpacking and hiking.
Ok, on the altimeter/barometer - Again, Ed is right that if you consider the altimeter and/or barometer to be mission-critical, get a Thommens analog altimeter. They are pricey, but they do not use batteries, and they are quite accurate (remembering that atmospheric pressure changes with the weather, so you have to learn how to do the calibration).
OK, so I haven't convinced you, and you still really really want a "wrist-computer". Having tried too many of them over the years and found that their effective lifetime is only 4 or 5 years at best, I will comment on my experiences -
You will grow dissatisfied with the Casio or HighGear pretty quickly. They are too limited in what they do. I had two Casios and found them to be pretty undependable and limited as far as the altimeter and barometer were concerned. Timex has some models that are pretty similar to the Casios, but more accurate and dependable (I use a Timex Ironman for my daily watch, and had a test version of the Timex WS-4 that I reviewed - it might suit your needs for not much above your price range).
Suunto's are pretty good and dependable. They do have the altitude, barometer, and compass functions you are looking for. I had a Vector for several years, then gave it to my son (he is still using it) when I got an X-6. I have used the X6 at some pretty extreme altitudes from Badwater in Death Valley (-200 ft or so) and up on tall peaks like Denali (20,320 ft) and Kilimanjaro (19,200 or so). The X6 has a computer connection, so you can see what your gain, loss, altitude vs time, rate of climb/descent, and barometric pressure are when you download after a hike. The Core series has many of the same features. And there are heart-rate monitor versions as well. I think Polar makes better heart-rate monitors that also incorporate the altitude and barometer functions. Both Suunto and Polar are pricey, but they are more precise (finer calibrations) and accurate in use. Both also come with GPS versions, if you get inspired to go that far. Polar's software is better than Suunto's for hiking and backpacking (that is, reviewing after you get back from the trip on your computer).