I ordered an upper from Del Ton (Wilson) and inspected the barrel and noticed that it isn't the SOCOM (HBAR) profile.  The barrel that I have is turned down underneath the handguard.  

Can anyone tell me what type of barrels does the military have installed on their M4's versus what I have?

By the way, I measured underneath the handguard, and the diameter is apprxoimately 0.67 inches.  My understanding that it is designed to save approximatley 1/2 pound.

Any reason to go with a "heavy" barrel?

That would be a standard M4 carbine barrel.  They are turned down beneath the hg just like the M16A2.  The SOCOM barrels were made in limited numbers for SOCOM only.  The rest of the big army has what you describe.