- An Olympic sprinter on a bad day runs faster than me on a good day.
is simply more colloquial than
- An Olympic sprinter on a bad day runs faster than I do on a good day.
which can be deemed to be more correct from a strictly grammatical point of view, with "I do" being used as a parallel structure to "An Olympic sprinter runs..."
Sentence (2) would be considered to be more correct by grammar purists because it shows the subject form of the pronoun accompanied by the proforma do.
The presence of the mentioned proforma avoids the awkwardness of using the subject pronoun alone:
- An Olympic sprinter on a bad day runs faster than I on a good day.
The awkardness of sentence (3) mostly arises from the presence of the subject "I" followed by an adverbial adjunt belonging to the predicate of that second clause without any linking. This would be formal but less awkward:
- An Olympic sprinter runs faster than I.