There are some very significant differences between the WIAT and the WJ-III. The WIAT is a graded test, meaning there are sets of questions for each grade and based on the number of points accumulated, a score is assigned. So if this child is in 6th grade, she will be given the 6th grade group of questions even if she is capable of answering the 9th grade questions.
With the WJ-III, it's the same test for everyone. So if the child is in 6th grade but can answer 9th grade (or 12th grade or whatever) questions, she is able to do so. The person being tested simply answers questions until they can't answer any more or they finish the test, whichever comes first. So in this sense, the WJ-III is a better test for a gifted child working significantly above grade level.
However, there are other differences as well. One that is pretty significant is the way reading comprehension is assessed. On the WIAT, the child is given passages to read and is then asked several questions about them (the passages remain accessible to the child so she can refer to them if she needs to). On the WJ-III, the child reads sentences that have a word missing and has to provide an appropriate word. Some kids have a very hard time with this task for reasons independent of comprehension.
I hope this helps somewhat.
