No - Postgres is faster and it has JSONB. (It also has tables and SQL and GIS and ...)
Because from my experience MongoDB was at least 10x faster and all of the benchmarks I've seen were using pre-WiredTiger storage engine.
You can take a particular application and compare performance when using two different databases on the back-end, but then the database itself might not necessarily be your bottleneck, it might also be the way the application is written. Because the database is only a part of the equation, the comparison also doesn't tell you anything about the performance of any other application.