As others have said - the weight difference is four ounces.
The RO921HB profile barrel (M4A1 SOCOM) has several advantages to offset the weight difference, however they're not necessarily critical for everyone, so it's kind of up to you whether you want the weight penalty. At the end of the day, they're both good, quality barrels, but they have the limitation of being military production grade chrome lined barrels.
The original onus behind the M4A1 HB profile barrel was because the "wasp waisted" government profile M4A1 barrles (RO921/920/977/6921/ect.) were bursting under heavy automatic fire (talking several continuous mag dumps during SOF break contact drills - think the end of Tears of the Sun - but y'know... more professional military and less Hollywood).
Part of the problem was simply the thinness of the barrel, but another part was because of the somewhat "odd" nature of the government profile barrel (thick in front - thin in the back) the uneven heat distribution was causing catastrophic failure. The point of failure tended to be right behind the handguard cap where the thin part of the barrel "flares" into the .750 FSB journal.
The solution was, therefore, to make the barrel thicker throughout and create a medium contour barrel (despite Colt's "HB" designation) that gradually flares toward the barrel extension, and eliminate the uneven heat distribution. Furthermore, making the barrel thicker resulted in the barrel taking longer to heat up to a critical level.
Additional benefits that came from the thickening of the barrel was the fact that the RO921HB profile is hypothetically more accurate (more precise, actually, but that's neither here nor there) than a comparable RO920 barrel not only because it resists heat better, but the thickening of the barrel makes it stiffer for its length than the RO920 barrel. Again, keep in mind that these are still military production chrome lined carbon steel barrels - so they're not exactly designed for precision and accuracy, but all other things being equal, a stiffer barrel will be more accurate.
Another side benefit is for suppressed use - 14.5" barrels, while very short compared to a 20" rifle are still pretty long tubes. When hanging a heavy suppressor on the end of the barrel, there's is POI shift to contend with, the suppressor changes the harmonics, as well as being a heavy weight at the end of a long lever - and consequently, as the barrel heats up, it will exhibit more droop compared to a barrel without a suppressor. As with the accuracy benefits - the stiffer the barrel, the more it will mitigate these problems. It won't eliminate them, but it will help.
As a counter to these benefits, however - during testing, it was found that the change in the barrel harmonics of the RO921HB barrel increased the potential for bolt bounce, necessitating H2 weight buffers as opposed to the H that was being used in the original RO921. While bolt bounce is a problem most often associated with automatic fire, it's still not something you want in a semi-auto system either. I tend to feel that an H2 buffer should be a companion to the RO921HB barrel and used together.
As far as personal use goes - I've long since used the RO920 and government profile barrels. Back before my suppressor days, I was so used to the government profile weight and balance, when I picked up an RO921HB barrel, I found the extra weight to be irritating - I knew about the heat and accuracy benefits, but for me, they were less important than maintaining the balance and weight I was used to. The difference is in fact not that severe, but I was pretty intimate with my RO920s, snuggling with them in the mountains and what have you.
Fast forward a couple years, now I do about 50% of my shooting suppressed and have gotten used to switching from suppressed to unsuppressed weapons - relative to the weight and balance change between a suppressed and unsuppressed 14.5" barrel, I barely notice four ounces any more. Also, for me, the biggest benefit for my type of shooting is the advantages that the RO921HB profile barrel has for suppressed shooting - mitigating droop and POI shift. The other benefits are "bonuses" and I'm in the process of slowly replacing most of my government profile barrels with M4A1 HB barrels.
Probably more than you were looking for, but hope it helps.
~Augee