What's the practical difference between a 16GB and 32GB iPhone?
There's no difference besides the storage capacity.
As the iPhone does not have an option to extend the memory after purchase, you have to choose the right amount of storage right from the beginning.
You can always manage how much space you use by manually choosing which data to sync (music, photos, movies, apps).
Generally more available space gives you the freedom of not having to manage your sync settings too much.

16GB should be fine for most people, especially if they are willing to make compromises regarding sync settings.
32GB is good if your like to take lots of photos or have a large music library.
64GB is good if you record HD movies which increase in size very quickly the longer you record.