I too have both, and have used them both on my MXT but only used the 10x12 back when I had a V3i. I even did a little bench comparison testing between the two, and here's my conclusion. They're both great coils. The best two big coils for the White's MXT/V-series. Both of them smoke White's 10" DD, lighter, deeper, better separation. Now between the two, the 10x12 has a tiny bit better separation, and the 13" Ultimate has a bit better depth. In my comparison testing, the Ultimate was consistently about a half inch deeper on dimes (both air test and in my backyard test garden). Maybe it's my imagination, but the 10x12 seems to give a "sharper" signal. A little more "surgical" if you will.
Can't really describe it, but I think the 10x12 has a narrower detection field at the cost of a tiny bit of depth, while the 13" Ultimate sacrifices the narrow field in exchange for a small bit of additional depth.
The differences are really small, they are both great coils. Overall, I like the 10x12 a little better for it's slightly better separation. But I keep the 13" Ultimate handy for when I want to squeeze the maximum depth out of my MXT.