I used to do a fair bit of qualitative eye tracking research a few years ago. (I was the guy you'd be "paying through the nose")
Mouse-tracking and eye tracking are very different. However, both can be used with the same goal in mind - to reveal telling aspects of user behaviour which can then be applied in improving the UI design of your system.
To say mouse-tracking is an alternative to eye-tracking is like saying a trowel is an alternative to a garden fork. Both tools are used in gardening, but both have their own strengths and weaknesses, and as a result they get used for different jobs.
Eye-tracking is viewed by most researchers as a niche tool - something that has its place, but not the tool you'd reach for by default every time. The only big exception is for consultancy firms that specialise in eye tracking - if all you have is hammers, everything you see is a nail. Particularly when each hammer costs $36,000.
Eye tracking is often criticised as an expensive way to evaluate your system. It also criticised as being easy to use poorly. It's "wow" factor often means that people are so busy being blown away, they don't real stopping to critically evaluate the real benefits of eye tracking over other approaches (like good old usability testing).
http://bit.ly/eye-tracking