Which has a greater influence on sound quality, the amp or the preamp?

Yes to both unless have a mid-fi or worse amp that will mask the change a preamp brings. 

Which is more important to walking? The left or the right leg? 

Not a good analogy.

But as,someone stated a good tube preamp does wonders to enhance the SS amp.

I’ve owned many different mid-fi and high-fi preamps and amps, both SS and tube.  All the components, and the mixture of components, can make a marked difference in sound. I personally like to keep the amp and preamp made by the same manufacturer and, of course, both being tubes.  Also, you must have quality loudspeakers to critically evaluate any changes in your system.

Everything is important but first upgrading the weakest link in your system will have the most influence!