The heavier barrel disipates heat better than a thinner barrel, however, once it heats up, it takes longer to cool down. This would be a factor for a prarie dog shooter or someone that is putting a lot of rounds down range.
I didn't say that a bull barrel wouldn't be more accurate, I said a 24" barrel wouldn't nessessarily be more accurate. I am no rifle guru but from what I understand having a stiff barrel does contribute to practical accuracy.
To be honest, I don't know how much the extra barrel length would give you in terms of velocity. I am guessing that it would be fairly significant. I have chroned my own ARs from 11.5" up to 20" and the jump between 14" and 16" seemed to be the most significant jump if I remember correctly. I don't have the numbers with me, I am at work. There was a difference between 16" and 20" but not a huge jump, not nearly as much as a lot of people make it out to be. So with that in mind, maybe the extra 4" wouldn't be that much of an increase, I don't know. Hopefully someone here will help you out. If not, maybe I can find something on it, or chrono my own 24".
I don't know anything at all about Model 1 or who makes their barrels. I would look into it a lot more before I spent any money. Check out AR15.com and see what they have to say about it.