What is the difference between FileVault 2 and Disk Utility Encryption?
Both, do the same thing, that is to encrypt your hard drive. However, the difference is in the approach and can be disastrous if you’re not careful with it.

Point 1: 

When you use the Disc Utility to create an HD with Mac OS Extended (journaled, encrypted) - it will “Format” the drive (any data that you have on it will be lost, forever), it will then ask you set up a password. Once you’ve provided the info, and click Ok. It will format the hard drive within minutes (depending on the disk size of course). This is faster, but a destructive process.

When you use FileVault - it encrypts the hard drive while maintaining the data within it. This is a slow and reversible (i.e. You can turn FileVault ON/OFF as you choose) process, often takes a few hours. But, if you need to preserve the data on the HD, then this is the way to go.

Point 2:

FileVault can be enabled in System Preferences > Security &amp; Privacy > FileVault to encrypt the existing data on the internal HDD on a Mac.

Disk Utility > Erase can be used to format an existing or new partition and encrypt the volume as Mac OS Extended (Journaled, Encrypted).

Conclusion:

If you’re concerned about the privacy of your files and user data, and your computer contains information that shouldn’t be seen without authorized access, you should absolutely use FileVault disk encryption.