I had an ESEE 6, wasn't for me, I now have a BK7. The 6 was cool, but I didn't like it as much as I thought I would. The handle scales don't have any contouring, and weren't the most comfortable for me in use. Really, something about the knife just didn't "click" with me. The sheath is greart though, and there's no doubt it's a quality knife, it just wasn't for me.
I find the handle on the BK7 to be more comfortable. In terms of capability, I figure both knives are pretty much the same. The factory Becker sheath works, but it blows compared to the factory ESEE sheath. However, for the price difference between the two, you can get something pretty nice. I've got some really nice custom kydex for my 7.
If you can, handle both knives before you buy, because that's what'll tell you which one you prefer. They can both do the same stuff in the bush. If you like the 6, go for it. If you like the 7, buy one, and if you hate the sheath, you can get a new one and be at about the same price as the 6. If the sheath works, then all the better. I was lucky when I bought my 7 and got on that still had the little Becker Remora in the sheath as well.
With that said, I don't use my BK7 much anyways though, it's a little bigger than I like to carry in the bush.