What is the pros and cons of these other than weight or what you can hook to them.
 What would be the best diameter of a barrel and does it being cut down under the hand gard hurt it? Is the H bar the best one ?

ya really gotta ask yourself what is the primary function of this AR goin to be? If it is CQB then ya want the lightest shortest AR ya can get, if ya are Varmint huntin, then a HB 20" would be the way to go.

I have a Franken-AR with a Bushy Superlight barrel, it is pencil thin all the way back. it is light and nimble , but it heats up pretty darn quickly , like 30rounds of rapid fire and it can get hot enough for ya not to touch it. As far as accuracy, if i can hit a pie plate at 100yards in happy, im not a competition shooter and dont care if all the holes touch, if i can hit my target im happy.

The superlight barrel is fine, but im not that happy with it, so im having a custom barrel made that will be Fat under the handguards (mid-lenght) and then pencil thin coming out. ill see how that works out. lol

The M4 can handle more heat than a super light but is lighter than a HBAR.  The fluted HBAR handles more heat than an M4 but is heavier.  I used to own an HBAR and wont own another.  Its dead weight.  I currently own an M4.  I might purchase a lightweight barrel in the future for a trunk gun/CQB rifle.