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

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!

The answer is "yes." How active is the preamp? How passive is the preamp? If there is gain, how is it done? What is the power supply, if there is one? Is there a DAC? Is there a phono preamp with gain? Is there a headphone amp? Are there filters? Is there a tube gain stage? How many dB? Selectable or not? Is there a balanced XLR input or output? On one extreme, you have the minimalist NVA preamp with no gain, all single-end input and output, no power supply. High-quality pot and source selector, a cabinet and that’s all. OTOH, you have a Pro-Ject Pre-Box RS2 with headphone amp, XLR in and out, dual DAC, I2S, USB, multiple filters, selectable tube stage with gain, remote, and a display and all in a cabinet less than half rack width.

This year my answers have changed to this question. Previously I would have said the amplifier, but that was because I did not own a high end preamp.

Amplifiers matter up to a point that you need to drive speakers efficiently without straining the amp; not pushing it into distortion. To my mind, that is an amplifier that can deliver high current; not just watts per channel. This year I added a CODA S5.5 solid state amp, and an Aric Audio Transcend "Push Pull" EL34 amp.....both capable of high current. They truly transformed my system, even with a "mid-fi" preamp.

Then a couple of months later, I added an Aric Audio Motherlode XL balanced preamp.....and I learned what all of the fuss was about with a high end preamp. It took all of the magic of the amps, and improved on most everything in every way.

I also believe that the room conditioning is of equal importance, so much that I'm building a dedicated listening room, with proper diffusion and absorption, dedicated power with high end receptacles. Once that is complete, then I'll review what needs to be changed.

Yes, the preamp is the heart of the system.

But I have always felt that the “2 hands clapping” are the speakers and the amp.

The contribution of the preamp is more subtitle and surely subtitles are central.

But, IMO, the “broad strokes” belong to the amp and speakers.

I used to be in the anti-preamp camp for a long long time. I had evidence that preamps don't matter at all, they make zero difference. At least I couldn't hear it. Until one day, I got one and plugged it in. 

I am still kicking myself for selling a Rogue Rp7 pre w/ top of the line NOS tubes.

I have a well regarded SS integrated now but definetly lost a little magic.