I guess one reason is that Java has to do everything itself (another aspect of platform independence). For instance, Swing draws it's own components from scratch, it doesn't rely on the OS to draw them. That's all got to take place in memory. Lots of stuff that windows may do, but linux does not (or does differently) has to be fully contained in Java so that it works the same on both.
Java also always insists that it's entire library is "Linked" and available. Since it doesn't use DLLs (they wouldn't be available on every platform), everything has to be loaded and tracked by java.
Java even does a lot of it's own floating point since the FPUs often give different results which has been deemed unacceptable.
So if you think about all the stuff C# can delegate to the OS it's tied to vs all the stuff Java has to do for the OS to compensate for others, the difference should be expected.
I've run java apps on 2 embedded platforms now. One was a spectrum analyzer where it actually drew the traces, the other is set-top cable boxes.
In both cases, this minimum memory footprint hasn't been an issue--there HAVE been Java specific issues, that just hasn't been one. The number of objects instantiated and Swing painting speed were bigger issues in these cases.