How do you manage big projects (hundreds of files) using only VIM?
I personally start having problems in any larger than small project.
I use a combination of NERDTree (directory sidebar), FuzzyFinder Textmate (go-to-file like TextMate's CMD+T), and Sessions (:h sessions) to help me deal with large projects.
I would suggest using some sessions helper plugin. I would mention what I use, but I'm not satisfied with it yet. Just Google "vim sessions".
One thing to note with getting FuzzyFinder Textmate to work is that it depends on an old version the FuzzyFinder plugin, specifically v2.16. Anything higher and you'll get errors. But it's definitely worth the trouble. While it doesn't have name completion, its search is smart so if I search for fro/time/actionsphp it will pull up the file apps/(fro)ntend/modules/(time)_tracking/actions/(actions).class.(php) (parenthesis denote what it's matching). It makes it very easy to pick out files that are only unique by their folder name.