There is a native JSON benchmark collection which evaluates speed, memory usage and code size of various operations among 37 JSON libaries.
The old performance article for RapidJSON 0.1 is provided here.
Additionally, you may refer to the following third-party benchmarks.
Basic benchmarks for miscellaneous C++ JSON parsers and generators by Mateusz Loskot (Jun 2013)
JSON Parser Benchmarking by Chad Austin (Jan 2013)