Does using the new FileVault use up less disk space than Legacy FileVault?
The two technologies share nothing except the name and cannot be directly compared.  The old Filevault created a spare bundle image file for your home folder, which was encrypted.  The new one simply encrypts the whole drive in a way that is invisible to the user.

If anything there may be a slight overheard to managing a sparsebundle which will not be there for whole disk encryption, but I doubt that it will be significant enough to make it a part of your decision to use it or not.