The biggest difference that I'm aware of is the lack of the Aero interface. Features like creating DVD's, scheduling backups, sharing docs, bitlocker, are not available in Basic. (also no home network or Windows Media Player).
You can always find free third party apps to accomplish some of these features, for example WinAmp for media, Carbonite for online backup etc),
If you already have basic and don't want to spend money, you can make basic work. If your comparing the differences, almost all reviews say premium is worth it.