The 2 great Rabbinic scholars of the 12th century were known as Maimonides (Rambam) and his frequent controversialist, Abraham ben David (RABaD or Raavad). Whereas Maimonides is well known throughout the Jewish (and non-Jewish) world, with hundreds of books about him, hospitals, and schools named after him and is a celebrated figure of Jewish intellect in areas of philosophy, medicine, astronomy etc. Rabad is scarcely known outside of rabbinical scholarship and the experts in halacha (and Kabbala) who study his original critiques of Maimonides.
Maimonides is known as a towering intellect, who was esteemed by surrounding Muslim and Christian cultures; as a philosopher whose magnum opus The Guide for the Perplexed is still the mainstay of Jewish philosophy and theology, and whose original 13 principles of faith have become a declaration of faith for the rabbinical orthodox world. Rabad was known as a great talmudist, who had the entire Talmud deeply ensconced in his memory, and he was reputed to be able to access any part of it on demand. He was the major rabbinic authority for France and Ashkenaz, whereas Maimonides was the authority for Spain and Sepharad.
Maimonides is considered a “Modern” orthodox proponent, because of his philosophical and rational thinking, his use of science and rejection of mysticism and superstition. Rabad, on the other hand, is largely claimed as a model for Ultra-Orthodoxy precisely because of his espousal of and expertise in Kabbalah, and his alleged disregard of science. However, neither of these stereotypes are necessarily true. I will argue quite the opposite.
A statement I have often heard from the Yeshiva world is that they follow Maimonides in halacha (legal interpretation) but not in philosophy. Indeed, the relatively modern Shulchan Aruch is largely based on Rambam's legal works. This statement, however, is problematic, because the one authority who is supposedly authentically Orthodox – Rabad – was also the chief critic of Maimonides' halacha, and not philosophy. Rabad leveled severe criticism against the “Mishneh Torah” of Maimonides, both methodological and substantive. The main methodological criticisms were that Maimonides was not providing sources for his statements, and that a text book of halacha is a bad thing, rather it should be derived through consideration of the various opinions in the Talmud. Indeed certain of Maimonides' statements seem to be in error (or fabricated) and Rabad will show that there is in fact much evidence to support the opposite conclusion.
The key problem with Maimonides is that he tends to present a strict position, when in fact the Talmud suggests a lenient or permissive position on many matters. He also seems to be aloof and unconcerned by the real world burden he is imposing on people, whereas Rabad is very concerned by the increasing burden of rabbinically added extras. In one famous controversy, Rambam is suggesting that a rabbinic Gezeira (added restriction) cannot be undone by a later generation. Here, the Rabad presents a case where this was precisely occurred since the reasons for that restriction were no longer relevant.
So whilst it may be claimed that Rambam was a Modern orthodox revolutionary, he was in practice an extreme conservative, who often presents halachic views which are impractical and unwarranted, whereas Rabad was the true revolutionary. Revolutionary is a relative term, since our impression of Rabbinic law is one of strictness and ascetism. Rambam, the philosopher was the ascetic, and he imposed an ascetic halacha, whereas Rabad, the Kabbalist was the most open minded thinker in the past 1000 years. His vision of Talmud was not one that strangles a person's humanity, happiness of enjoyment in this world – this was the conclusion that Rambam reached. Rabad viewed the Talmud as a way of living and allowing people to fulfil there lives in this world, and not to wait for the next. Hence, it is my view that Abraham ben David was the true Modern Orthodox revolutionary.