Perhaps the difference is admission to a specific school or admission to a school's gifted pull-out program or gifted class. Perhaps it's just a matter of proving to teachers and administration that our children are different and needs something different in their education. Or perhaps test results are required for participation in some extra-curricular experience such as a Distance Learning, Super Saturday or Summer Enrichment Program for gifted kids. On the other hand, if the results of the test are only to satisfy parental curiosity, there may be no reason to test the child. This is a difficult question for many reasons.
Some schools only accept certain test.
In those cases, using a different test would not be of much value, at least to the school. Some states require a specific tester rather than a specific test, such as Pennsylvania's current law that requires the tester to be a Certified School Psychologist. Again, testing using a professional psychologist in Pennsylvania who is NOT certified as a school psychologist would be of little value, at least to the public schools. Some tests have limitations that make them inappropriate for certain populations, such as a test with a low ceiling being an inappropriate test for gifted children. For gifted children, the best age to test is when knowing the test results can make a difference.