It has been a while since I first dreamt about a reliable way to complete C++ code within vim. Sure, there was omnicppcomplete, which was able to complete more or less accurately from ctags databases, but the quality of the completion was greatly dependent on your coding style (I never could get myself used to put all my methods declarations on the same line). What we missed was a clever completion plugin, something that would be able to look deep inside the code, to resolve the types of the object you are refering to and to provide the set of accurate methods. Actually, we needed a plugin that would have the same knowledge the compiler has. That is a huge task, which is probably the reason why it has been let aside for so long. But recently, almost at the same time, two plugins have appeared, based on this idea.
The first plugin, clang_complete, uses a feature from the compiler clang++, from the llvm project. This new C++ compiler aims at being as reliable as g++. Though as far as I know, it is still not ready for production, it recently compiled boost, so expect to hear about it again. clang++ features the ability to complete a given line of code from the command line, and our first plugin is based on this feature: see http://www.vim.org/scripts/script.php?script for more information.
The second plugin is based on a crazy gcc modification called gcc-code-assist. The author has hacked in gcc's code and provides a replacement for gcc that also builds a sqlite database at the same time you build your code with it. Then a command line tool called gccsense allows to query this database. Basically, you just replace gcc with gcc-code-assist in your makefile, and you install the plugin provided on the author's website: http://cx4a.org/software/gccsense/. The modified gcc is really easy to compile, I even made a package for archlinux that you can find on AUR. Obviously, this stuff is very unlikely to make it to gcc's upstream...
So, what to use? Well, if clang++ builds your project without errors, I'd go for it, because this is for sure a feature that will continue to be maintained by the llvm crew. Otherwise, gccsense should work exactly like gcc-4.4. Honestly, I did not have the chance to really test any of them, so it will be difficult to provide good feedback for me. If someone has the opportunity to test it, please leave a comment!