I'm biased (I was raised on Bach) but I've always thought that most of modern western music owes an enormous debt to J.S. Bach. He pushed even temperament, was ridiculously prolific, represented music across Europe to the point where he was known as "Grandfather Bach" in some royal courts, and his music was often inspired by patterns, numbers and complex riddles.

There are a huge number of famous musical passages, hooks, licks, etc. attributed to artists from Mendelsohn to the modern day that can be found in just the Well Tempered Clavier. Listen to the second half of BWV857(http://allofbach.com/en/bwv/bwv-857/) which is fugue number 12 from the Well Tempered Clavier vol 1. Tell me if you don't hear something familiar there :-)

Paul Graham's essays discuss how the most exciting work in many media was done by the generation that invented them. For example, the most interesting paintings were done centuries ago, when oil paint was new. Bach is like that. When he was writing, the piano was a new invention, and a system of musical scales had been found that allowed you to change key mid piece, without retuning your instrument. Those things are old now, but Bach lets you feel the thrill they gave when they were new.

von Bulow said something along the lines of Bach being the old testament of piano music and Beethoven being the new testament. Bach for the first stage of development and Beethoven for the end of the development stage.

Maybe an answer to OP could be Beethoven is a reaction to, or maybe, completion of, Bach's work. Or Beethoven is a bit more playful and experimental than Bach in general?

Or TLDR is physical development of the instrument didn't end with Bach it ended with Beethoven. So its kinda hard to talk about one without talking about the other.

I think it's his use of coutnerpoint and its ability to pleasantly overload the brain. Case in point, Toccatta and Fugue in D Minor. Close your eyes and try to play air organ to this: http://allofbach.com/en/bwv/bwv-565/detail/