See I spent some of today researching between the BK2, BK10, and BK7. Most people say they are all decent choppers. The only intimidating thing about the BK7 is its length. It's really long. The Largest knife I own is probably my smaller sized Kabar. Right now I feel I'm leaning towards the 10 or 2 because everyone claims they're next to indestructible and extremely capable of the majority of tasks you would encounter outdoors.
"Most people say they are all decent choppers" - Don't believe this.
If you are doing light "chopping" by holding the handle on the back end with two fingers (and maybe a lanyard for safety), these short knives can give you some decent bite if the edge-geometry is sufficiently slim (not really the case on any of the large beckers or anything from ESEE), but that does not make them "choppers", just not enough length to go with the heft. If you skim a couple of those LMFII videos in my last post, Noss does some "chopping" into wood and concrete with the knife.
You are much better off setting the edge against the target and then smacking the spine of the blade with a mallet, i.e. batonning - much more efficient and also safer, and you can do that with your ESEE-4 just fine. Carry a baton or use the knife to make one in the field.
But if you are really planning on chopping with your knife, consider getting a knife built for it, a "camp knife". Again, lots of options, including the BK7 (which is on the short end of knives built for that) as well as amazing customs available. It's time to grow your collection!
Here is a video of the new (2016) GSO-5.1, at 11:00 I use it to chop down a couple of saplings in two swings per tree, but the trunks are a mere 2-3" in diameter and the geometry of this knife is excellent (5-dps primary down to only 0.020" behind the edge). This is "light chopping" that the BK2 and LMFII both suck at due to the shorter length and more robust geometry.
[video]https://youtu.be/gYWafo6EoTM?t=11m[/video]