To illustrate the difference, in that picture:
Top is a Government profile barrel (Pencil under the handguards, thick past the front sight post.) This is what you see in military M4s, M16s and C7s
Middle is a pencil barrel (Thin all the way down). This was the original AR15/M16/CAR/C8 profile.
Bottom is an HBAR (Thick all the way down) Typically seen in Competition rifles/DMRs/Short secret squirrel carbines that need the rigidity for suppressors or the heat resistance from seeing a lot of automatic fire.
Basically what it comes down to is "improved accuracy" and the ability of the barrel to withstand "over heating".
Between Pencil and HBARs, to a degree, yes. If you're only going to be sitting at a competition firing line, HBAR is the better choice for accuracy. If you're actually going to be carrying the thing, Pencil is the way to go, the weight difference is astounding. Easier to point, easier to hold on target, you can carry it all day long.
The gov't profile barrels came about after some US military testers misread some gauge results, and mistakenly concluded that barrels were bending from bayonet use. They "corrected" this by thickening the barrel from the bayonet lug on out. By the time they realized that the barrels were actually fine, new production barrels were already rolling off the assembly line, and they figured having a tougher barrel probably couldn't hurt.
In my opinion, the gov't profile makes little sense. But it's what the military uses, so those wanting something authentic should look no further. That thick front looks pretty nice as well, lining the barrel silhouette up flush with the A2 flash hiders, without the weight of the HBAR. There's nothing wrong with preferring the aesthetic!
the m4 profile barrel with the 203 cuts is the 14.5" SOCOM barrel which is a bit beefier (withstands more heat during f/a and much more accurate
Theres the M4 SOCOM profile, which is an HBAR and the M4 profile which is gov't. The 203 cuts actually seem to be known for minor accuracy issues - they apparently cause some bad vibrations which can throw shots. They put up with it because they need that '203 compatability.
But it's what the US military uses, and it looks wicked. Again, nothing wrong with liking the aesthetic.
I'm surprised the C7 isn't using a Hbar barrel. I've shot ar 15 sporters 20 inch Hbar. Very nice gun.
Try carrying it for days then get back to me. It's a trade off to be sure, but pencil and gov't profile barrels are plenty accurate, and of all the complaints about those early pencil barreled M16s that fought the Vietnam war, overheating on full auto wasn't really one of them. They're not belt feds! As long as you're not dumping mag after mag after mag, the pencil barreled ARs can take it.