A person who is impelled has been persuaded to do something (perhaps based on moral grounds) and does so at least partially of his or her own volition. Compel implies that the person being compelled has no choice in the matter and is being coerced. For the person being compelled, the coercion is so strong that choice and morality don’t enter into it.
Surely we won’t need a third cataclysm to impel us, at long last, to take serious action? [Weekly Volcano]
Schwarzenegger then sought a court order to compel Chiang to honor the order. [Reuters]
The bridge-burning effect is the underlying fear that seems often to impel journalists not to print unflattering information about their sources. [The Daily Athenaeum]
He stressed investigators cannot legally compel anyone to talk. [The Chronicle-Telegram]