What is the best occupation to utilize a degree in Engineering?

Bio mechanical engineering because in the future an aging population with health care issues.
1) Software/firmware use/coordination
2) Improve medical tech with through mechanical means (even nano)

Define "best". :D

"Best paid relative to length of education" is either computer engineering, or the kind of chemical engineering that is involved in oil field work. Of course, those are the numbers for now, things may be different after you've done your degree(s).

"Most interesting work" depends entirely on your interests. If you want to make nuclear power plants better, or redesign bridges, or come up with new materials for prosthetics, those are all varieties of engineering you can go into.

"Most rewarding work" also depends on your interests, specifically in terms of what kinds of problems you want to fix.

Also define "occupation". Folks with engineering degrees can do lots of jobs, even ones that aren't obviously engineering-related but still very valuable. In addition to being an actual engineer (someone who develops and/or implements technologies), you can go into design, management, consulting, lots of things. :)

Engineering degrees are valued in a lot of career fields. The analytics skills gained in engineering are valued in financial services, marketing, as well as traditional technology companies.