There are numerous normed test instruments for reading diagnostics. WJ III is highly recognized. Whether it is the best diagnostic to use for a particular individual is not a question I can answer.
Is difficult child's Learning Disability (LD) in reading?
Within WJ III, there are several reading subtests. You've only mentioned two. Are these the only ones that were performed?
See http://www.wrightslaw.com/advoc/articles/tests_measurements.html#table1 for conversion chart and other test measument information.
Argument for using the same test instrument: Every test instrument is different. In order to compare apples to apples, and oranges to oranges, the same test instrument must be used. Your school district is aware of this.
Examples: WJ III compared to scores from a WJ II would not necessarily be an accurate comparison; the same with WISC IV compared to WISC III; Stanford-Binet 5 to Stanford-Binet 4th Edition; and so on.