... I just think there's more to XNA than a convenient wrapper around DirectX, and I'm wondering if Monogame is more than just a convenient DX wrapper as well.

SharpDX is the convenient wrapper around DirectX, and MonoGame builds on top of that to give you the high-level API that is XNA compatible.

There's a pretty article on CodeProject that discusses how to move from XNA to MonoGame, and its limitations. But is sure looks like MonoGame is the (cross platform!) future of XNA.