Assent and consent are mostly synonymous—they both mean to agree or to give permission—but assent connotes a greater degree of enthusiasm, and consent often comes with reluctance. In law and government, consent is more readily denied, while assent is often a mere formality.
One may readily assent to part of Koppel’s 1987 assertion: Humanity needs the Truth, and human beings need moral absolutes. [The New American]
Venezuela issued a decree banning use of President Hugo Chàvez’s name and image without his prior consent. [Fox News Latino]
The province’s 2006 Pharmaceutical Act, which received royal assent but has yet to be proclaimed in force, would allow pharmacists to write prescriptions, administer drugs, and order and interpret diagnostic tests. [CBC News]
New Push for Ireland to Consent to a Bailout [headline, NYT]
In the second and fourth examples, the consenters have greater degrees of authority. In the first example, assent is used synonymously with agree; in the third, assent refers to a royal formality in which the Queen’s agreement is a foregone conclusion.
When there is doubt, consent is usually the best choice. It is much more common than assent and seems to cover a broader range of uses.