well, i'm not dead sure of how classes are implemented in PHP, but I assume they are the same as in C++ and perl.
A class, in short, allows you to organize your code better and lets you create relations and groupings better. Performance wise, creating classes in PHP will not be useful or fast unless you are doing complex stuff with your code. For simple fetch-from-the-db-and-print stuff, go with functions.
If you're writing a large piece of software which requires multiple instances of the same code, use objects.
Let me know what you plan to write and I can let you know whether I prefer functions or classes. And please check out all the articles and tutorials on OOP with PHP! Some of them also discuss the performance issue.
-sridhar