Which type of air rifle propellant source is the best?

There is no simple answer... Every type has some pros and cons. You need to decide. I've prepared a summary, it may help you to make a decision.

CO2 12g cartridge

+Works out of the box

+One 12g CO2 cartridge gives you ~20 nice shoots. From 20 to 40 shoots pellet speed is decreasing much faster, after 40 shoots you lose about 20 FPS per shoot.

+You can keep a couple spare 12g cartridges inside your pocket because they are small.

+Air gun is mobile, no tanks, no hose.

+Almost no points of failure.

-Small CO2 tank have bad temperature stability. If you shoot fast and the tank has no time to heat up from the environment, it is getting colder. Colder tank means less pressure inside the cartridge, so air rifle power is decreasing while shooting. After a couple magazines, when whole liquid CO2 is vaporized, pressure is decreasing rapidly.

-Small tuning capability.

CO2 425g tank

+Bigger CO2 tank has better temperature stability, big aluminum tank has better heat transfer coefficient, so it heats up faster from environment. Pressure inside the tank should be more stable.

+Connect once, shoot the whole day, disconnect at the end. One full SodaStream tank (425g CO2) is equal to 35 standard cartridges. It has more than 1000 shots.

+No more low power shoots after a couple magazines when liquid CO2 ends.

+Shooting may be cheaper. In my country 35x12g CO2 cartridges cost 12 Euro. Refilling a SodaStream tank in a big market is 9 Euro, in a local gas shop it is 3 Euro. Refilling by yourself from a big 6kg CO2 tank is 1 Euro.

+Medium tuning capability.

-Needs some investment.

-Bottle connected by hose to the gun, so you are less mobile.

-Bigger bottle, you need to carry it to the spot with a hose and valve.

-Couple points of failure.

PCP tank

+Constant pressure and power when tank is equipped with pressure regulator.

+Cheapest way of shooting, you can pump it with hand pump. No more buying CO2 to shoot.

+With adjustable pressure regulator, you can easily adjust power of air rifle.

+Huge tuning capability.

+/-You have 100~120 shoots with 14J power from 0,25l PCP tank.

-Needs the biggest investment

-Bottle connected by hose to the gun, so you are less mobile.

-Bigger bottle, you need to carry it to the spot with a hose and valve.

-More elements, more points of failure.

Let's start with ... tank temperature drop

Here's how tank temperature drop looks during shooting. The way how I measured 12g CO2 cartridge is less inaccurate, but it shows some nice results.

Blue line shows speed of 12g CO2 cartridge temperature drop. It drops much faster than big CO2 tank. As expected, because a big aluminum tank with a lot of liquid CO2 has much better thermal stability and heats up much faster from environment. Big tank (Red line) rate of temperature drop already starts slowing down to reach equilibrium point.

Why is it important? Check how much CO2 pressure drops when temperature is decreasing.

FPS stability

Stable pellet speed is very important for accurate shooting. Here's how FPS stability changes when you change the power source of an air rifle.

In the chart, you see how much pellet speed drops while using CO2.

Blue line shows 12g CO2 cartridge. You have about 20 "stable" shots. After it, the cold effect starts and causes pressure to drop. I think there is less and less liquid CO2, cartridge is cold, so freezing effect speeds up. After 40 shots from the start there is no more liquid CO2, so pressure starts to drop rapidly, about 20 FPS per shot.

Red line shows big CO2 tank. As you see, pressure drop is still present, but there is no rapid FPS drop - there is A LOT of liquid CO2. The big aluminum tank should be in equilibrium after some shots. It has better ability to heat up from environment, so after some shooting FPS should stay at constant level. Personally I was thinking that, it will be more constant than 12g cartridge. There may be one more thing: CO2 cartridge cools down the whole air rifle down tube, so putting new CO2 cartridge to cold tube will add more cooling effect. With an external tank this is not a problem.

Yellow line shows PCP mode. FPS trend line is constant, so you will always shoot in the same place. Small FPS speed variations are present because air regulator is not perfect and sometimes pressure may vary a little.

Tuning capability

Depending on chosen propellant source, not all mods are available.
With a 12g CO2 cartridge, you can increase power a little, by adding a softer valve return spring. During hot day you will get extra 1J, but temperature drop will reduce this extra 1J to smaller value. A more powerful shot makes a bigger temperature drop. Expect max 12J.

With an external CO2 tank, you can increase power much more, by adding a softer valve return spring and removing the cartridge piercer. During hot day you will get extra 5J, but temperature drop will reduce it a little. More powerful shot makes bigger temperature drop. Expect max 15J.

With a PCP tank, you can increase power a lot. You can achieve this by adding a softer valve return spring, removing the cartridge piercer and adding a hammer spring spacer. Expect max 25J. After drilling transfer port, barrel port and valve, it may be even more. With a ridiculously strong hammer spring, you can reach 30J, without playing with the transfer port.