If I calibrate with "matrix" mode and run the profile validator I get delta-E's of 40-50 for each color.

If I calibrate withe "LUT" mode I get delta-E's of 0.1-0.3.

First, can someone explain the difference in the modes (or point me to an article).

Second, I realize the delta-E's aren't totally useful here since I am using the same device to check it's own profile, but why the wildly divergent numbers?

They are actually pretty useless in terms of tying to gauge the quality of the profiles.

How do gradients and other images appear when you assign the profile to the docs and view them in Photoshop?

Do you mean assign the monitor profile to the documents using "convert to profile"?

I tried that and I don't see any banding in a gradient image with either profile.

No, Assign Profile. And the test should be done based on this PDF:
http://www.ppmag.com/reviews/200412_rodneycm.pdf

Thanks for the link.

The matix mode gives me better separation in the blacks (4-6) vs the LUT (6-8).

Both seem a bit to the greenish side in the greys, but it felt like my eyes would adjust for it if I didn't step through too quickly.