Hi Adam --
Glad to be here, thanks for taking the time to post your questions. This is a good one!
I have no actual hands-on experience with a Warre hive - but still I have a comment or two on the concepts involved.
First of all - there are some interesting differences and some important similarities between the two hive types.
The most obvious difference is that a Warre hive is a vertical hive, while a top bar hive is a horizontal hive. (No kidding, right?

)
The most obvious similarity is that they are both "foundation-less" hives - the intent is to allow the bees to make their own natural beeswax comb - no wax-coated plastic, pre-printed foundation is employed in either hive type.
Since the whole focus of natural beekeeping is that "IT'S ALL ABOUT THE WAX!" I think that Warre hives are a fine idea. However, read on for a few more thoughts.
The reason that I haven't used any Warre equipment myself has to do with the idea of "nadiring" to increase the size of the hive. Nadiring is a fancy word for adding space (in this case hive boxes) to the BOTTOM of the hive stack, as opposed to "supering" or adding to the TOP of the stack.
Since in nature, the bees build down from the top of whatever cavity they are occupying, nadiring actually makes good sense. But while the idea sounds good on paper, they lost me when I tried to picture how I, as a lone woman beekeeper (I often work my bees by myself) would be able to add a box to the bottom of the stack without dismantling the whole hive, or devising a complicated piece of equipment to lift the whole stack at once so that I could place the new box below it without dismantling the entire brood nest box by box. This troubles me because another philosophy at work with the design of the Warre hive was to avoid disturbing the brood nest by taking it apart to inspect, which is of course, less disruptive for the bees.
One last remark: There's a design difference - that comes from the vertical vs horizontal question, and that is this: The bars of a top bar hive must touch. No air flows between the bars in a top bar hive, it all stays beneath the bars, which make a sort of roof.
In a Warre hive, the bars cannot touch - as the bees must travel up and down between the boxes. This makes a Warre hive a bit more like a Langstroth hive, and brings with it the interesting air flow and condensation issues inherent in a vertical hive. That is what necessitates the "quilt box" at the top of a Warre stack. So while I DO think of a Warre as a foundationless hive, I DON'T really think of it as a top bar hive due to this difference.
Make sense? If you want to "nadir," then you pretty much give up the idea of leaving the brood nest undisturbed, OR you find a way to lift the whole stack in order to place a hive box on the bottom. It just seemed simpler and easier to me to work horizontally at counter height level and avoid all the heavy lifting in the first place.
Bzzzzzt!
-- Christy