Exact meaning of "Too good a/of a X" clause and etymology

In UK English I usually hear "too good a."

In US English you will find both "too good a" and "too good of a." There is still a preponderance of the former.

The expressions are equivalent.

As for the history of the phrase, look here.

In American English, they're not equivalent in register; "too good a" is more formal and appropriate for writing, while "too good of a" is informal and less appropriate for writing. It's conversational.

I found a comment on the inappropriateness of "too good of a" in an advice column, This Is Not Too Good 'of a' Usage, and evidently the Oxford Book of American Usage and Style says the same, but unfortunately the e-book I found started with the letter "p" and the explanation is under the entry for "of."