Let's take an example of each. In Jeanne DuPrau's City of Ember (MG), 12-year-olds face a wonderfully daft rite of passage called Assignment Day. It marks the end of their schooling and the beginning of their working (adult) life. The kids literally draw a job out of a hat. The protagonists, Lina and Doon, eventually get the jobs they've been wanting (after a little trading) and joyfully embark on the next phase of their lives as contributing members of their society. There is a little training period but it amounts to learning the trade.
In Veronica Roth's Divergent (YA), all 16-year-olds must choose which faction they want to live and work with for the rest of their lives. After the selection ceremony, though, the real rite of passage begins--the faction initiation and basic training. Those that don't pass end up homeless (or dead). During the training / testing, the protagonist, Tris, questions whether she's made the right choice. Is she one faction or another, or is she something else altogether?
To me, it seems like in YA, the protagonist questions, avoids, and/or transcends the rite itself. The teen years are about exploring your identity—and cultural expectations for it. If you’re choosing a faction to be with, for instance, you have to think about whether this is where you belong—and more importantly is that all that makes you you. In other words, the story is really about defining yourself despite cultural expectations as well as the ability to think beyond your programming. (Tally in the Uglies series is another good example.)
In MG, though, the protagonists seem to embrace the next stage of growing up. For instance, Lina and Doon don't question their new roles in the society of Ember (well, until they realize it’s doomed, of course.) Ditto with Jonas in the Giver. He too plunges into (though a tad reluctantly) the role of Giver (in training) until he learns how flawed his Utopian society is.
So maybe that's the key difference. Both YA and MG protagonists ultimately question their dystopian societies. However, YA rites of passage are more identity-driven whereas MG ones are more about belonging.
What do you guys think?