Java and C# easily outclass Phoenix i performances, if only because they are statically typed, but also because they run on VM's that are more advanced (and admittedly older, so more optimized) than BEAM.
Java and C# outclass performance in raw CPU work certainly. Phoenix does not do raw CPU work however, it is primarily a web dispatcher on top of cowboy and the BEAM will run circles around both Java and C# systems if they are programmed to anywhere near the same quality of failure handling that the BEAM implicitly supplies (/me has worked with both Java and the BEAM for over 10 years).
Also, the Erlang VM is older than the JVM, initially created in the late 1980's. The JVM, according to wikipedia, was introduced in 1994. Also the BEAM has significantly better GC handling that both the JVM and .NET both since it has a segmented memory model (each actor has segmented memory) unlike the JVM and .NET's monolithic Heap's, this allows it to perform vast optimizations that ensure that the GC is almost never called yet memory is properly and fully reclaimed due to the bounds of the individual Actor heaps, and even when the GC is called it does not stop-the-world or anything of the sort and has multiple layers of GC's that run for specific cases, the system stays running even as the GC's (rarely) runs. The average GC run time even when it does run is measured in the single-digit 'micro'seconds. If anything the BEAM VM is not only just much older than the JVM and .NET VM's, but also more advanced.
Java and C# incur more much more developer complexity for web development than Phoenix.
And as the the sibling comment points out, raw CPU performance isn't the only measure of efficiency. The JVM loves to eat memory, and if you get 100x CPU efficiency but use 10x the RAM, you're still bounded on machine resource usage by that memory usage.
