First question:
Which circuit is more affected using unmatched tubes ?
the cathode bias circuit or the fixed bias circuit ?
This is the wrong question. The
Library of Information has RDH3 and 4 available for download. RDH4, chapter 13, section 5(v) on pages 580-581 discusses the effects of mismatching.
What you really need to ask is, "what class of operation and tube type is most affected by mismatching?"
The effects are most serious when you're using pentodes/beam power tubes in class AB, but the result will be some higher amount of distortion (most likely increased even harmonic distortion) and less power output. The section of RDH4 cited discusses class A triodes. In it, they use an example of using two entirely different types of tubes on either end of a push-pull output stage; one of the tubes has twice the transconductance and half the plate resistance of the other tube. This would be equivalent to having one new tube, and one nearly-dead tube in an amp.
The result? 2nd harmonic distortion, which would be zero in a perfectly-matched and balanced output stage, was only 5% which is a common design target for "low distortion". So there is no serious effect, with class A triodes.
We're not given info in RDH4 about how much power output was reduced compared to matched triodes.
So now on to your question: I'd suggest mismatching is more of a "problem" in a fixed bias circuit.
You can't assume a class of operation by the bias method, but it is more likely to see cathode bias used on class A or hot class AB amps, and fixed bias on cooler class AB amps. That's largely because cathode bias is inherently safer, cheaper to incorporate, and does work well deep into class AB. For deep class AB and higher power outputs, you generally need to use fixed bias to prevent the bias from changing materially with large plate current swings.
Further, if you use a pair of tubes with a single cathode bias resistor, they tend to find an average point where both tubes are happy. If the cathode resistor is adequately bypassed, then the differences of plate current swing won't upset the bias. Again, you might get a little more distortion, and a little less output power. It might not be enough of either to hear a difference (or only a very slight difference).
Very severe mismatching (one tube in the socket, the other tube not in the socket) could lead to power supply hum and output transformer saturation, because the hum cancelling effect of push-pull is based on equal hum currents flowing in both halves of the transformer primary. The possible increased saturation would be because push-pull OTs are not made for unbalanced d.c., and the balanced d.c. implied by push-pull allows for a smaller core for the same output power. Most push-pull OTs allow for some amount of unbalance, however.
Second question:
often I see fixed bias circuit with doubled bias pot to be able to regulate the bias voltage for each tube, question: which is the best regulation procedure to obtain best results ?
What LooseChange posted. If you are concerned, you can have a bias adjust pot for each tube.
It occurs to me that even with the idle currents made equal by the individual bias pots, if the tubes are
very mismatched, you will still have the same issues I mentioned. "Very mismatched" implies very different bias voltages required for equal idle current, which means each tube can handle a different amount of input signal before serious distortion. So you might not get every last fraction of a watt. It might, however, sound good to have each tube beginning to distort at a different time, and by a different amount.