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

I've gotten the most noticable differences in system sound based on (descending order of magnitude)

Speakers/Headphones 

Room (for stereo listening)

DAC/Cartridge 

Subwoofer placement/integration 

Phono stage

Amplifier (tube types)

Preamplifier (with/without tube type)

Streamer

I haven't done DSP but do have a DIRAC unit collecting dust and based on what others say it could fall somewhere between subwoofer integration and amplifier.

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.