Luke DuBois at Hindsight Is Always 2020 has charted the most common words used by each of the presidents. The results are historically embedded, but the differences are fascinating. Here's the most common word used by each president:
Van Buren: results
DuBois doesn't include Obama in his analysis, but the Boston Globe made "wordles" for several of his speeches. His most commonly used words in speeches from 2009 to 2011: nation, people, Americans.
Interesting contrasts among back-to-back presidents: limits / enemy, mutual / bank, slavery / emancipation, alliance / tonight, terror / nation, truly / barrels. Other than that, no comment.