I would disagree with Handel as “Staid.” His concertos alone are quite daring in many ways; but his music is serious and somewhat in the traditional sense. I would definitely agree that Mozart can be characterized as “Exuberant.”
It’s hard to describe Handel in a single word. He could write works as lilting as The Harmonious Blacksmith, as soaring as the Messiah, and as stodgy as some of his later oratorios. Maybe I’ve judged him too harshly ...
Handel is the master of baroque melody. Bach, the master of music in its purest forms. I play through various chunks of the WTC every night before moving on to Beethoven or Chopin and find something else in the way a phrase can be formed (Bach lets you do this) that changes the nature of the prelude or fugue.
Most composers give you exacting directions in the music, but Bach you get a very white canvas. You get notes, and rests (what the Japanese call the "Ma") and not much else.
The interpretation depends a great deal on one's knowledge or conception of baroque performance norms. The Bach of Czerny or Busoni is quite different than that of Andras Schiff or Gustav Leonhardt. But I would argue that they are all valid - at least in the case of Bach.
The nature of absolute music is that it is endlessly adaptable. Harpsichord, Concert Grand, Swingle Singers, Bela Fleck, Wendy/Walter Carlos, hot Russian chick with a guitar https://www.youtube.com/watch?v=olW6-jhSgMg, Stokowski with a full romantic orchestra, Mozart string quartet transpositions...
No other composer has that universality.
Still, Handel writes a better show tune.