Ways ''not'' to prove that your GoldenHammer is better:

* X can be written in terms of GoldenHammer; therefore, GoldenHammer is better. Problem: TuringEquivalency is rampant. Problem-2: Being better at mirroring other techniques may not extrapolate into being better for everything. Example: Many compilers and interpreters are written in C. However, this does not mean that C is best for everything.

* GoldenHammer is more "elegant". Problem: Impossible to objectively measure.

* "It's the rage". Problem: You cannot vote the world flat.

* It is based on a simple base or "atom" that is used to make everything else. Problem: simple parts has not been proven to always lead to simple results. (All else being equal, having simple bases is desirable, but we don't know if it is equal.)

* Toy examples show GoldenHammer solving problem X in fewer steps. Problem: Example may not be representative of real-world problems or all domains.

* It's better for this one little metric, and therefore it is summarily better. SovietShoeFactoryPrinciple.
** But note that it's perfectly legit to say: "It's better for this one little metric, and therefore there is this one more little bit of objective evidence that it is better".  Enough such cases constitute a lot of evidence.

(more to come...)

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See also: HowToSellGoldenHammers