Thank you guys for the replies.
Some days ago I was flying with a captain and we actually had this case. I was PF and he insisted in using Vx up to FL100 while I believed Vy would be a better option, although if it would had depended on me, I would had just set minimum clean speed and end of the story… As someone pointed out, this is totally a theoretical discussion, since obstacles or conflicting traffics were not involved.
Anyway, once brought the discussion to the cockpit I argued Vy would allow us to reach FL100 in less time so we could turn earlier towards our destination, resulting in less flight time, therefore less fuel. He would choose Vx based on a shorter distance would result in less fuel burnt.
The airplane was a B737, and Boeing doesn't provide as far as I know, a way to calculate fuel burn for Vx or Vy so I can't conclude which one is more fuel efficient. And I ignore if there is a way to calculate that regardless of the specific airplane, simply based on generic flight conditions information (speed, altitude, etc).
What I know is that on one hand Vx is Vmd for a jet, that is, the most economical speed for an aircraft, so flying constantly at Vx would result in the less fuel consumption. On the other hand Vy allows to be less time in low altitude, which for a jet results in a lower fuel consumption.
Now, which of these two factors is more dominant? I don't know…