I was reading the comments on this answer and I saw this quote.
Object instantiation and object-oriented features are blazing fast to use (faster than C
Your questions don't have concrete answers. For example, C++ does not define memory management at all. It leaves allocation details up to the library implementation. Therefore, within the bounds of C++, a given platform may have a very slow heap allocation scheme, and Java would certainly be faster if it bypasses that. On another platform, memory allocations may be blazing fast, outperforming Java. As James Kanze pointed out, Java also places very little constraints on memory management (e.g. even the GC algorithm is entirely up to the JVM implementor). Because Java and C++ do not place constraints on memory management, there is no concrete answer to that question. C++ is purposefully open about underlying hardware and kernel functions, and Java is purposefully open about JVM memory management. So the question becomes very fuzzy.
You may find that some operations are faster in Java, and some not. You never know until you try, however:
In practice, the real differences lie in your higher level algorithms and implementations. For all but the most absolutely performance critical applications, the differences in performance of identical data structures in different languages is completely negligible compared to the performance characteristics of the algorithm itself. Concentrate on optimizing your higher level implementations. Only after you have done so, and after you have determined that your performance requirements are not being met, and after you have benchmarked and found (unlikely) that your bottleneck is in container implementations, should you start to think of things like this.
In general, as soon as you find yourself thinking or reading about C++ vs. Java issues, stop and refocus on something productive.