I've never been able to prove to myself that in general terms, Java is faster than .NET. I've run a few of my own benchmarks that indicate quite the opposite, but even then, I'm not willing to make such a blanket statement.
I can say that in pure code execution, .NET executes faster that Java on the same machine, at least the last time I bothered to test about 2 yrs ago. Code written in C# incidentally executes a little faster than VB.NET because C# doesn't have all the type checking that VB.NET does.
The algorithm I used to test was basically a string parser that took a string which was an arithmetic expression, transformed it into reverse polish notation, then determined the answer (stuff taught in many schools). Even doing my best to optimize the code in Java, I could never get it as fast as even the VB.NET code. Differences were around 10% as I recall.
That said, I've not benchmarked GC or other aspects and never have been able to dig up good unbiased benchmarks that actually test either in a real-ish system. Usually you get someone trying to prove why their religion is better and they ignore any other view point. I'm sure there's some aspects of Java where they have better algorithms that will nullify the raw code execution speed.
In short, when people make statements like that, ask them to back it up. If they can't or rely on 'everyone knows it', don't bet the farm on their statements.