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 morality doesn’t enter into it.
Examples
These writers use impel well:
Surely we won’t need a third cataclysm to impel us, at long last, to take serious action? [Weekly Volcano]
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]
And these writers use compel well:
Schwarzenegger then sought a court order to compel Chiang to honor the order. [Reuters]
He stressed investigators cannot legally compel anyone to talk. [The Chronicle-Telegram]
Compel is sometimes used where impel would make more sense—for example:
Ryan insists the right on-air talent will help transform WCFS into more of a “companion” to listeners and compel them to stay tuned in longer. [Chicago Sun-Times]
And in this weird case, the writer, apparently in an effort to avoid using propulsive and propel so close to each other, uses compel where he clearly means propel:
. . . and composer Hans Zimmer, whose propulsive score helps compel the action forward. [LA Times]
