I don't know about Muslims memorizing the Quran, so I can't answer your request to compare the two kinds of memorizing. You have already received several good answers to your question. read more
There are many Jews who memorize The Torah in several different contexts. The actual Torah Scroll is read at least 4 times every week, since Hebrew has no vowels or accents we memorize the proper melodies and pronouciations from a specilized Torah. read more