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FX Crown STX Superlight Barrel

It depends on the power level and projectile weight. If the .22 and .25 are set to the same power level, the .25 will be quieter because the larger bore has more expansion volume at the same length. If the power levels are proportionate to the bore area, then the .22 will be quieter, because it uses less air. So, this question cannot be answered in a vacuum.

A moderator will make whatever system you have quieter. How much depends on how much power you are tuned for, and how large the moderator is. Some moderators are better than others, at the same size; so that detail matters too; as do your expectations.
 
The difference in performance will depend to some extent on the tune used. For the same tune, the shorter barrel will shoot at a lower velocity, but not 5/6 x of the longer barrel. Such a dramatic difference would only occur if you are tuned to reach maximum power with both barrels.

You can retune with the shorter barrel to get the same velocity as the longer barrel, but the air rifle would then use more air to achieve that velocity, and accuracy may be slightly reduced. Certainly, the shorter barrel tend to be louder than the longer one, at the same tune; and especially at a "hotter" tune to restore the velocity to match the longer barrel.

When the tune is optimized for the given barrel length, there should be no difference in accuracy between the longer and shorter. You will get smaller groups if you d not drive a given airgun too hard; meaning too close to its maximum power. To quantify what velocities you can expect from given slugs and slug weights, you will need to talk to people who own FX Crowns, or similar air rifles with 500 mm .22 barrels. It may be possible that FX Factory or distributors could offer tuning advice too.


Not a Crown, but potentially transferable tuning info, here: