IMO, the most often overlooked facet of tube amp design is the power supply. An amp with a power supply exhibiting good regulation, very low impedance, fast response without overshoot and oscillation, and plenty of current reserve will sound COMPLETELY night and day different from the exact identical amp circuit with a poor power supply. My personal experience has been that the power supply is responsible for about 50% of the amp's overall character and presentation. The power supply can make or break such things such as soundstaging and imaging ability, bass weight, slam, and speed, and mid/high coherency and focus. The other half is up to proper amplifier section design, the quality of the output transformers and componentry, and the tubes themselves.

As j rodney stated, the componentry used in the amp circuit, especially the signal path, has a huge bearing as well. For example, using carbon composition resistors and paper in oil caps in the signal path will sway the signature in the direction of warm, full, and rich. Using metal film resistors and Teflon/tin foil caps will lean towards clean, transparent, and analytical sounding. Of course, the output iron's gotta be the good stuff, too.

All in all, you can build a better sounding amp with "everyday" tubes and a humdinger circuit, componentry, power supply, and output transformers, than you can with the trendiest boutique power triodes or NOS sweep tubes and crummy stuff. I guess that maybe gave away my personal answer, the circuit matters more, IMO.

Thermionic