I’m a walking inconsistency, I suppose, because I’ve got a 7 pound M4A1-profile LE6920HB. 
There are a number of different ways of looking at the weight issue, and usually – almost always – less is more. Still, there are cases where a bit of weight isn’t unwelcome, and my early SP1 Colt carbines always struck me as a bit “whippy” at the muzzle back in the 80s. To some degree, you need to consider how much you wish to modify the weapon: a 6721 with a ShortDot or CompM4 strikes me as a near-perfect rig, but if you’re going to hang lights, lasers, night optics, VFGs, magnifiers, trailer hitches and who-knows-what-else on it, then weight will quickly become a relevant concern.
For hunting here in Germany, I favor a reworked G.33/40 (small ring 98) mountain troops/fallschirmjaeger carbine in 8mm Mauser that weighs next to nothing, yet fires a very heavy recoiling round – but I’m only firing it two or three times in an outing. I can handle the momentary pain for the convenience of something that is extremely easy to carry all day long. Well, actually I take some perverse pleasure in the swift kick when it comes time to pull the trigger, but that’s just a side issue. LOL
For defensive/carbine work, the recoil of the 5.56mm isn’t really an issue, but the heft and handling certainly are. Both the 6920 and the 6721 are excellent choices, and in a perfect world, a guy would probably own one of each. Which is best-suited to your needs is a question that only you can answer, but for a lightly-modified carbine with excellent stability and target tracking characteristics, I would seriously give the 6721 a long, hard look. It remains perhaps the most underappreciated variant in Colt’s entire lineup, and the longer I’m around the A3 Tactical Carbine, the more I like it.
The price surely isn’t hard to take, either. I’d call the 6721 the little-known “sweet spot” at the top of the AR market; doubly so, when you consider that 99.9% of the 6920’s we all pay a premium for will never have an M203 mounted to that ridiculously all-consuming (for purely cosmetic reasons) stepped barrel notch.
Chief