Learned, scholarly, erudite are comparable when they mean possessing or manifesting unusually wide and deep knowledge.
Learned implies the possession of knowledge gained by study and research; it usually implies wider and deeper knowledge than do such words as educated, cultivated, and cultured, and is usually applied to those who are conspicuous in their class or profession for learning, to associations composed of such persons, to books or articles written by them, and to periodicals edited by them or publishing articles by them.
Scholarly also implies learning, but it is applied particularly to persons or to the utterances, ideas, and writings of persons who have attained mastery in a field of study or investigation, who have to a greater or lesser extent advanced knowledge in that field, and who have exhibited consistently high standards in the appraisal of their own and others' discoveries.
Often, more narrowly, the term implies great care for accuracy or exactness.
Erudite, though often employed as an equivalent of learned or scholarly, usually implies a love of learning for its own sake, a taste for what is out-of-the-way or remote from the interests of the average well-read man, and often an inordinately wide range of knowledge.