It would depend on if the database backed up contains Enterprise features or not. If not the backup should restore with no problems. The question doesn't say that there are such features used in the database.

The books online page http://msdn.microsoft.com/en-us/library/bb964719.aspx indicates that every edition of sql server 2008 can restore a compressed backup, though only 2008 Enterprise or 2008R2 Standard and higher can create the compressed backup