Although both bands get classified as "progressive rock", they are so different that I think comparisons are, not so much odious, as devoid of meaning.
I once made a list of my personal favourite prog bands, and the Moodies and Yes came in at 4 & 5 respectively.
Yes are undeniably prog, in fact they are almost the very definition of prog. The Moody Blues on the other hand are not such a clear-cut case. Their claim to "progressive" rests largely on their mixing of rock and classical styles with orchestral arrangements, and in particular on the album "Days of Future Passed", the first really successful album to blend musical styles in this way. While some of their later albums might have features excellent music, they could simply be characterised as well arranged rock songs.When you get to albums like The Present and beyond, I don't think there is much left that justifies the prog tag; it's pop, or rock, whichever you prefer.
Both bands did excellent stuff, and both also did a certain amount of rubbish. "Apples and oranges" is such a cliche, but in this case it's true.