I can see him being more pushy than Wilson about getting us into World War I. But I can also see more pushback from congress. He would have pushed for that stupid amendment to elect U.S. Senators by popular vote. But I'm not sure he would have been nearly as enthusiastic about the income tax.
Neither TR not Wilson were all that popular by the time the 2016 election rolled around. FWIW, Wilson was the first two term president to be elected with less than a majority of popular voter. Clinton was the second. BO was the only one to do worse the second time around.
Haad Teddy won, we might not have a Federal Reserve or the “Progressive” Income tax, either.
Hard to say, but he would have been better for the USA than Mrs. Wilson!
And, had Teddy won, we might be a better country today!