In some cases, managed code can actually be faster than native code. For instance, "mark-and-sweep" garbage collection algorithms allow environments like the JRE or CLR to free large numbers of short-lived (usually) objects in a single pass, where most C/C++ heap objects are freed one-at-a-time.
From wikipedia:
For many practical purposes, allocation/deallocation-intensive algorithms implemented in garbage collected languages can actually be faster than their equivalents using manual heap allocation. A major reason for this is that the garbage collector allows the runtime system to amortize allocation and deallocation operations in a potentially advantageous fashion.
That said, I've written a lot of C# and a lot of C++, and I've run a lot of benchmarks. In my experience, C++ is a lot faster than C#, in two ways: (1) if you take some code that you've written in C#, port it to C++ the native code tends to be faster. How much faster? Well, it varies a whole lot, but it's not uncommon to see a 100% speed improvement. (2) In some cases, garbage collection can massively slow down a managed application. The .NET CLR does a terrible job with large heaps (say, > 2GB), and can end up spending a lot of time in GC--even in applications that have few--or even no--objects of intermediate life spans.
Of course, in most cases that I've encounted, managed languages are fast enough, by a long shot, and the maintenance and coding tradeoff for the extra performance of C++ is simply not a good one.