That's really hard to claim. Both are languages, and don't have inherent performance characteristics, C# can even be compiled to native for some targets.
There are some aspects of C# (such as value types) that can give an advantage of idiomatic C# over idiomatic Java, but for anything performance sensitive you aren't going to write idiomatic code anyway, you'll be writing pretty convoluted code with SoA instead of AoS and so on.
As for the respective VM:s, the CLR vs the JVM, the performance differences are pretty small. You wouldn't rewrite from Java to C# for performance.
My understanding is that C# made a number of good decisions surrounding structs, but that the JVM has had a huge amount of engineering work, and the HotSpot JIT & GC options are better performing.
Can you point to any compelling evidence that either language is faster?
There are some aspects of C# (such as value types) that can give an advantage of idiomatic C# over idiomatic Java, but for anything performance sensitive you aren't going to write idiomatic code anyway, you'll be writing pretty convoluted code with SoA instead of AoS and so on.
As for the respective VM:s, the CLR vs the JVM, the performance differences are pretty small. You wouldn't rewrite from Java to C# for performance.