This makes me even more confused because I'd suppose Mary and Elizabeth's schooling to be similar.

Sort of, in that it was fashionable at the time to educate aristrocratic girls in a similar way to their male counterparts, but also dissimilar in a couple of ways. First, Mary was Henry VIII and Catherine's only child - she was obviously privately taught at home and with an eye to her future as the wife to a powerful man. Elizabeth, however, was educated to a large degree alongside her brother Edward, destined for the throne. So, in a way, Elizabeth got a man's education, much more so than her older sister would have.

Second, Elizabeth and Edward were taught by Roger Ascham, who used a novel way of teaching language - he would have them translate something into English, then back into the original language again.

edited because my brain doesn't start working until my coffee does....

She possessed nine languages so thoroughly that each appeared to be her native tongue; five of these were the languages of peoples governed by her, English, Welsh, Cornish, Scottish, for that part of her possessions where they are still savage, and Irish. All of them are so different, that it is impossible for those who speak the one to understand any of the others. Besides this, she spoke perfectly Latin, French, Spanish, and Italian extremely well.

Source: Venice: April 1603 Pages 562-570

Calendar of State Papers Relating To English Affairs in the Archives of Venice, Volume 9, 1592-1603. Originally published by Her Majesty's Stationery Office, London, 1897.

http://www.british-history.ac.uk/cal-state-papers/venice/vol9/pp562-570

I'm skeptical that Elizabeth "spoke" more than a few languages, such as English, French, and Italian, fluently. Nine languages, as cited below, seems like the kind of hyperbole that stalks famous monarchs. However, Elizabeth appears to have been instructed in a number of languages from an early age, her pedagogy involving "double translation" or translation from one language into a target language and then back to the original or another language. It should be remembered that vernacular grammars were a product of the sixteenth century and languages such as Welsh were not reduced to grammar until the seventeenth. Her passive language skills (listening and reading) were undoubtedly higher than her active (speaking and writing).

Here are some useful quotations from the Oxford Dictionary of National Biography: "The flattering memoir of Anne Boleyn composed by her chaplain, William Latimer, reports that she intended her daughter [Elizabeth] to be well trained in languages, ‘that she might in after tyme be hable sufficiently to judge of all maters and embassages.' Accordingly, ‘she wolde endewe her with the knowlege of all tounges, as Hebrue, Greeke, Latyne, Italian, Spanishe, Frenche’" (‘William Latymer's chronicklle’, 63).

Also: "Ascham's pedagogy was founded on the principle of double translation, both out of and back into classical and modern languages, and Elizabeth's early and precocious exercises were in this vein. Between 1545 and 1548 she regularly made translated texts her new year's gifts to her father, stepmother, and half-brother, the authors including John Calvin and the Italian reformer Bernardino Ochino."

She might have been a fine translator, but again, I'm skeptical that this resulted in spoken fluency in so many languages.