By performing a hypothesis test on a sample from a normal population, you find that the hypothesis $\mu = 20$ cannot be rejected at $10\%$ risk. A colleague obtains the same conclusion by testing $\mu= 22$.
I think this is the weakness of the test: several hypotheses may not be rejected. Am I wrong?
Verifying a null hypothesis without expliciting an alternative does not make sense.
Then, to compare your test with your friend's one you can calculate the two $p_{value}$'s.
A test is measured by its $p_{value}$.
If the alternative is a simple hypothesis too, you can also calculate the power of both tests to compare them