[Note: this is a subjective response but the question itself tends to invoke subjective responses by nature].
C++ is a multi-paradigm language and there's a lot more to it than OOP. However, to suggest it's simply better than C is a bit... bold. :-D In the hands of an experienced C coder, and for the right purposes, C code can be very elegant and simple. Consider the Lua interpreter which is coded in C; it compiles to a very small binary which would have likely been a lot bigger even in the hands of an equally skilled C++ programmer, and is therefore well-suited for embedded use. C generally won't be as safe (ex: implicit casting, requires manual resource cleanup, etc) which is one thing which C++ strives to do a little better than C, but it also won't burden the programmer with awkward casting syntax (in C++ one shouldn't need to cast often, but in C it's quite common), e.g.
On the other hand, and I'm trying to speak very generally, C++ can actually make it easier to write more efficient code, particularly for code that needs to work across multiple types. The qsort vs std::sort benchmarks are a classic example of this and how C++, through templates and inlined function objects, can provide cost-free abstractions. In C one would have to write a separate sorting algorithm for every type by hand or stuff it in a macro to achieve comparable results.
Most C++ programmers who migrated from C never look back. I might be an oddball, but I still find C to be useful for implementing small scale libraries. For a start, it's a bit easier to port and builds super fast. For these kinds of things, I take implicit casting for granted. I would hate to work with any C code on a large scale, however, and have unfortunately have to do this from time to time.
As for specific differences, sepp2k already pointed out a pretty comprehensive list.