I see what you mean. Look at it this way, Windows mobile is being replaced by a new OS in the fall, so even if you stay with windows you might have to do a little learning of the new software, and who knows whether your current apps will translate to it (they probably will, but check with the developers first).
Android is an entirely different platform. in many ways it is more efficient and stable (and cleaner) than windows. However it lacks built in support for some of the corporate software that windows systems dominate. If you need to have your system integrated into an existing medical network, you might want to check with that system's administrators firs. It is quite likely that widows microsoft might be their prefered system.
Now as to android apps, the issue with them is not that they are unstable. the issue is that the android market is in some ways playing catch up to the apple App store. The app store has had 3 years to develop applications. in addition, apple's very stringent requirements essentially keep apps off the store until they are 100% ready for use and perfectly polished. The android market is much less restrictive (maybe it is a conscious decission to facilitate expansion?). App developers are able to upload beta versions of apps, and continue to develop them, through updates, with feedback from android users. in theory this leads to a better app and one that people want to use. The thing is that the android market has a ton of apps in beta stage, as well as a bunch of finished apps that occasionally get updates pushed to them. Who knows whether the apps you needs are even available for android. Lastly the Android market is set to recognize the version of android on your system and will only display those apps that have been determined to run on your particular version. you can get around that, but depending on what you download, the app might or might not work perfectly (or at all).
It sounds like you nee to do a little digging to see whether the specific applications you use for work are available for android or can be ported to it. If they are, then you would probably be better off buying a phone with the latest versions of Android and relatively high hardware specs (thus avoiding compatibility issues). Lastly, you need to find out whether android is supported by the network you need to access with your machine.
Do that or run a similar search for windows mobile 7 and microsoft's upcoming Kin products, which might be better suited to your needs.