In reply to jwhepper:
Well, I'm a US climber but I don't know what "all" US climbers do. I certainly see more and more guide-type devices being used, and we've had a few of the lowering accidents that are associated with that technology. I suspect that the guide plates are the wave of the future, especially as more multipitch climbs get bolted belay anchors which, in addition to being of almost unquestionable strength, will also be positioned at the appropriate height for guide-plate belaying.
In the Gunks it isn't infrequent to have low anchors, in which case a belay off the harness seems better. It is also easier on the arms in many cases, there being a fair amount of friction pulling ropes through guide plates (the round cross-section carabiner David mentioned is essential). Moreover, I at least can do a much better job with two climbers in situations in which one might be moving up and the other down, using a harness belay rather than a guide plate. Now that we have various "assisted braking" devices that sort of or actually do lock when the rope is loaded, one gets some of the advantages of the guide plate belay with the harness belay (but letting completely go of a brake strand, as is common with the guide plates, is still not an option).
(By the way, when I say "harness belay," I mean the device clipped to the rope loop (not the harness belay loop) and the tie-in tensioned so that the load is transmitted directly to the anchor. So this is really belaying off the anchor too, with the addition of the energy-absorbing connection of the belayer's tie-in.)
I've noticed what I think may be a psychological downside to the guide plates: belayers anxious to use them may build high anchors in spite of the fact that better (and sometimes much better) low anchors are available. This is not entirely hypothetical, I've seen a few examples.
No one has mentioned this, and maybe a generation is coming that won't even be aware of it, but I dislike the belay I get with most users of guide plates. The plates act and are treated as ratchets, so the rope is pulled up until it is tight and then, rather than being backed off as is usual with the harness belay, it is just left under tension. The follower continually has the sense of being pulled, which may be a good thing for guided clients, people trying to speed climb, and alpine ascents in general, but on ordinary crag climbing it just interferes with the experience of climbing the route. Moreover, if the rope runs diagonally or out over a roof, being pulled can become a serious pain in the butt and even in some cases a bit dangerous.
Another aspect, which is again psychological rather than intrinsic to any of the plates, is that their semiautomatic nature promotes what we would formerly have called "inattention" but now is celebrated as "multitasking." Whatever you want to call it, the downsides haven't changed.
And finally, there is the warning that the guides plates probably won't lock if the rope runs horizontally out from the belay anchor, i.e. if the pitch ends with a protected traverse to the belay.
For all these reasons, I'd hope that folks just learning the ins and outs of multipitch climbing will not give short shrift to harness belays, so that they'll be able and willing to use them effectively when they are appropriate. That said, on climbs with mostly or entirely bolted anchors, the plate-swapping techniques described by David are surely the fastest and most efficient method for swapping leads.
I've got a shiny new DMM pivot and am interested to see the extent to which it changes the picture I painted above. One question will be whether you can lower with it with less likelihood of a very sudden release. Another is whether it will be easier for a belayer who forgoes fashion and decides to be attentive to easily manage slack and so avoid or at least ameliorate the ratchet effect. And of course there is the question about how much the resistance to pulling ropes through the device will be reduced.