Which aspect would you respect more in an office?

Competency is the word your looking for.

The point is to ask, if a Degree is not important while doing the task; it should be unimportant during hiring/salary discussions as well

At my company now i look for experience and maturity. When i was a manager working for a company i look for degree. The bigger the brand the better. The main reason is easier to blame when things go wrong. Feed thier ego, Tier 1 people bend over backwards to get things done or find reasons to blame some one else.