Owning only the BK9, I can't say from personal experience, but the BK1 certainly appears to have been intended to be more of a heavy chopper than the BK9, being as it weighs 3.5 oz. more (22 oz. vs. 18.5 oz.) and has a more weight-forward design. The BK6, although longer than either the BK9 or BK1, is made of thinner stock, and actually weighs .7 oz. less than the BK9. Like most machetes, the BK6 should be better suited to cutting light vegetation than to heavy chopping.
Beyond that, the BK9 will be the more versatile tool. For one thing, compare the ricassos - the BK9 essentially doesn't have one. Because of this, and the outstanding (IMO) design of the Becker handles, you can choke up on the BK9 and do some pretty decent precision work for a knife of this size. I've also found the BK9 to be excellent for two-handed, drawknife-type use, and like many, find a straight edge such as the BK9's more practical than a recurve.
One more comment on chopping ... I think a lot of it depends on how you like to chop. With a knife or even a small hatchet, I prefer to chop with a lot of wrist action, which gives me greater control. So not only do I not get the same advantage that others would out of a tool that's very blade-heavy, but I find them more tiring. And with a BK9 that's properly profiled and sharpened, a short, quick chop mostly from the wrist gives me probably 85%-90% of the penetration in a piece of wood that I'd get with a full swing using shoulder and arm anyway.
YMMV, of course, but the BK9 has really impressed me.
Dave