I know what you mean. In fact, the parish in Tulsa in which I was chrismated (and in which I participated in the Nativity liturgy this year) sang Joy to the World and Lo, How a Rose E'er Blooming after the liturgy (not during, of course!). While that may offend the ears and sensibilities of many on this forum, it had been a tradition in that mostly-Lebanese, ethnic parish for easily longer than I've been alive (25 years). So while that parish is most likely a rare bird in that regard, it does feel gratifying to hear some of the "old songs" (ironic, no?) I grew up with.
Having said that, I think my "ear," as it were, is still very western, though I be in an eastern church. The Russian tradition of the OCA is, in general, much more to my liking musically than the Byzantine flavor of the AOAA or the GOAA. While they don't belt out Good King Wenceslas, I find much of the ooomph of which you speak to be more present in the Russian tradition.
This is, of course, the highly subjective and admittedly biased opinion of someone who also adores the Western Rite in general and in Orthodoxy in particular and who needs his "fix" of gregorian chant every so often, so I'm sure there are others out there who find a "Byzantine Nativity" more than satisfying.