I have been reading in a few places that air filters get better with age, is this true? And how much better?
No, not for any reasonable definition of "better."
Think about what an air filter is designed to do: stop all particles that are larger than some known cross-section (often measured in microns). Anything smaller than that value will be trapped by the filter and unable to proceed.
Let's use an extreme example: you've covered your air filter in fine gravel (e.g., from a fish tank). Clearly, this is now an "aged" filter that has prevented a bunch of nonsense from passing it.
However, you haven't increased the net filtering capability of this mess in any significant way. Remember, a filter is supposed to pass everything smaller than a specific cross-section. However, you haven't added a significant number of air channels that are smaller than that measure. As a result, the net effect is not something that's "better" at filtering out particulates.
What you've likely done, however, is plug the functional air channels that were present. A filter in the intake path of a functioning engine is effectively a vacuum sucking those particulates against its air channels. If you intentionally add a bunch of mess to the filter, you'll plug those air channels. The result is less air getting to the engine which is combined with less fuel and resulting in less performance.
So, if your goal is equal or better engine performance while running on ever better intake air quality due to a nasty old air filter, it's not possible. You can use a dirty air filter to progressively strangle an engine over time but I doubt that's anyone's definition of "better."