Was asked this question by a Muslim today and was in the company of several other kinda-educated Christians and we had at it for a while.
My friend Peter who is a young whipper snapper said something about grace and works which was profoundly unsatisfying to me.
Here was my attempt: The fundamental difference is regarding the nature of grace, or more specifically, how we received or participate in God's grace. Catholics (and Orthodox) believe that one receives God's grace primarily as it is mediated through the sacraments which are communal and visible.
Protestants (or at least evangelicals) believe that God's grace is not mediated by anything, and is primarily received when one receives grace in his heart and mind as an individual who agrees with certain statements about Jesus and the Bible.
Which prompted her next question, What do you mean when you say grace (na3ma)? And after figuring out how to say "deserve" in Arabic (thanks Abu Elias!) I said, "Mercy is when you don't get what you deserve, grace is when you get something you don't deserve." (Ripped that off from a Bible church pastor back in Texas.)
Peter the Young Spring Chicken later made a more sensible proposal about Protestantism: Protestants privilege a forensic model of justification. That may be the start of something of interesting, but it needs more fleshing out.
I think that talking about the authority of Scripture is a red herring for this question. I think it does really go back to grace, and specifically how we receive it or participate in it. I like focusing the discussion on this question because it gets around facile statements about works and grace, and especially the Reformation "solas" which are fine for riling up masses but not useful (at all) when it comes to the hard work of actually doing theology. In other words, we can skip that annoying, "You believe in works salvation!" and ask the more useful question, "Why do you believe that grace is primarily mediated by the sacraments?"
