If you want personal experience, I have some, not much:
Very important for calculating fractals is accuracy.
I wrote an LR-Decomposition once in C++ and Java
with the exact same calculations and (!) comparable accuracy, which means
the same number of fractional digits used.
Some of the "intersting" matrices I tested were singular depending on C++,
in Java I could easily compute the inverse matrix, which had to be impossible in C++.
(I checked it, don't worry, Java was correct there, A*A^-1 = I was alright.)
That's for accuracy,
speedwise the programs were comparable, Java was neither slower nor faster.
So Java even had the advantage there
Another test I once made was a simple prime-calculation.
Same algorithm and C++ needed ~5000 ms. for the primes between 2 and 1.000.000 (Was a simple program, not optimal)
Java needed only 3500 ms.
What's also very important: Every language can be slow, depending on how good you are with it.
I use Java many years now and think of C++ as a ugly language, harder to read and with a crappy error-handling.
So I will always be faster with Java than any other language, especially when using GUI's (very easy in Java).
The only interesting alternative in my point of view would be some GPU-programming, but I don't know where to start
and learning that would consume a lot of time, that I currently don't have...
Give me some examples, where C++ or any other language is faster than Java (you experienced yourself)