k4 (21)
{.Q.A@<<>#:'.Q.a#=_x}
{.Q.A@<<>#:'.Q.a#=_x}@,/0:`:e
"EITUSALNROMCDPVGQBFHJKWXYZ"
This approach uses the builtin alphabetic constants .Q.a (the lowercase letters) and .Q.A (the uppercase) to do the filtering and translation back to upper. The process:
_: convert to lowercase (leaves non-letters untouched)=: group into associative array of characters and their indices.Q.a#: take only lowercase letters (includes empty lists for characters that did not occur)#:': count each value in the array>: get the keys of the array ordered by its values, descending<<: find the position where each item would appear if the list were sorted.Q.A@: apply that list of positions back to the list of uppercase letters
The last two steps are conceptually a bit tricky; they basically allow you to permute one list according to another. See the q documentation for rank for more details.
(Note that if we stop before the translation back to uppercase, we have a correct result, but in lowercase:
{>#:'.Q.a#=_x}@,/0:`:e
"eitusalnromcdpvgqbfhjkwxyz"
and a code length of 14!)