Look here Compare Windows 7 Editions
Here is what Ultimate has that is not available in Professional:
BitLocker, BitLocker To Go, AppLocker, Direct Access, Branche Cache, MUI language packs, boot from VHD.
Here is what Professional has that is not available in Home Premium:
Domain join, Remote Desktop host, location aware printing, EFS, Mobility Center, Presentation Mode, Offline Folders, Group Policy (GP) controls, advanced backup, XP Mode.
If you know what those are and need 'em, go for it.
The default recommendation is Home Premium.