A lot of people seem to get a big kick out of the word “shat,” even though “shitted” is a much more eloquent variant.

I certainly see the appeal. Shat would seem to be the standard and historic preterite/past participle of everyone’s favorite smelly verb, and so its presence in a sentence inevitably invokes a nice bit of tension between the strict gramatic traditionalism and the inevitable vulgarity. (It even works when constructing haughty blog posts!)

But shitted is poetry; much more expressive, funnier, a surprising and livley addition to any BM-related anecdote.

BRIAN: And then who walks into the Bratskellar? BAM! Wayne Brady!
FRANCIS: What did you do?
BRIAN: I totally shitted myself.

or

GRANDMA: I just shitted that entire bag of Sugar Free LifeSavers.

As with anything, much depends on the rythm of the sentence, the relationship between fellow nearby words, adjacent phonemes, etc.. But pounds for donuts, shitted is a far more engaging option. Try it with friends.

BONUS!
In Canterbury Tales, Chaucer uses “shitten.” Not bad!