Although power supply of guitar amp commonly use traditional simple capacitor filer circuit , the power supply is still the most important part of the amplifier. Because ultimately, it is the power supply that decides the capality of amplifier as a whole.

Power supply of amp
The power supply of amplifier includes three parts: Power transformer, rectifier, filter. The usage of power transformer is transforming the wall AC voltage such as 110v or 230v into the different voltages which tubes needed.
The function of rectifier is converting AC into DC.There are two kinds of rectifier according to the electronic components they used: tube and solid state. More about rectifier, we will discuss in other article.
The current passing through rectifier still has ripple which frequency is 50 hz or 60 hz , caused hum in the amp possibly. So it need the filter to cancel or reduce these ripple.There are two common power filter configurations: capacitor filter and choke filter.
The ripple voltage is often expressed as a percentage of the maximum DC voltage. A typical figure might be 10% for a push-pull amp or 5% for a single-ended amp, though this is highly dependent on individual circuit requirements of course.

Capacitor filter VS Choke filter supply of amp
A capacitor is a device that stores electrical energy in an electric field. It can be used to absorb and store energy when the AC power is higher than what is needed by the DC load and to supply energy to the load when the AC power is lower than what is needed. The capacitor working is based on voltage, it filt the voltage,remove as much power ripple as possible, and maintain a constant DC value . Capacitor filter is consist of resistors and capacitors. It has the better filting resultion dring working at small current and high voltage statment.
A "choke" is the common name given to an inductor that is used as a power supply filter element. They are typically gapped iron core units, similar in appearance to a small transformer, but with only two leads exiting the housing. The current in an inductor cannot change instantaneously; that is, inductors tend to resist any change in current flow. This property makes them good for use as filter elements, since they tend to "smooth out" the ripples in the rectified voltage waveform. Choke filter (LC) is consist of resistor and choke.It is prefer to big current circuit.

Why modern tube guitar amplifiers replaced choke filter by capacitor?
Many vintage amps used choke filters in their power supply. Fender was interested in maximizing voltage in order to maximize clean output power, so many Fender-derived amps even use a choke-capacitor (LC) filter to supply the power valve screen grids. An LC filter is a second-order filter, so it provides steeper attenuation of ripple than an RC (first order) filter.
The technique winding choke is simple during early period of amp, but it is difficult to make electrolytic capacitor. Although tube is also voltage component tending to use capacitor in power filter, they have to use choke filters.
Currently, the technique making electrolytic capacitor has developed. It is not problem to make big capacity capacitor. Other side, the cost of choke become high in the pace with the price of copper high. Although the life of chokes is longer comparing capacitor, weight, mounting space/orientation/hardware/labor, and wires make a less desirable widget for mass production.
Since many people like metal style which need amp more overdrive, there is no need to squeeze out every last watt of clean power, so many guitar amps use RC filtering for the screen grids, which is much cheaper than using a choke.