I wouldn't call either of these knives "large" but I guess they are a bit larger than the average knife, so I could see why you would call them that.
If I was choosing between these two, I would go with the Becker. The main reasons would be cost, and ergonimics. The BK2 is much cheaper than the ESEE 5, while still having similar quality of the blade steel. The main difference is that the ESEE 5 comes with a few "extras" already on the knife (kydex sheath and micarta handle scales). These extras can be added the Becker later, and you'll end up paying about the same for the BK2 as the ESEE 5 at that point.
After that, its the ergonimics. I feel like the Becker line of knives has an amazingly comfortable handle design. It seems more people like the handle design on the Becker, but I could be off on that one. Also, as far as the warranty, the ESEE 5 has an unconditional lifetime warranty, so if you break it, you get a new one. The Becker on paper has a little more restrictive warranty, but effectively its about the same. I would say both have great warranties. The few Beckers I've ever heard of breaking were replaced under warranty, so I don't think its a huge differentiating factor.
And finally, the big difference between the ESEE 5 and the BK2 is the grind. The grind on the BK2 is higher, so it should be a bit more "slicey" then the ESEE 5. Neither of them are moras, so keep that in mind, but my BK2 has done all the woods work I've ever asked it to.
Here is what the BK2 stock sheath looks like BTW. Nothing amazing, and nothing really bad.
And finally, if you're looking for a large knife for chopping, I would actually look for something a bit larger than these knives. Something like the BK9 or one of the machete type blades out there.
In my tests the BK9 out chops the BK2 by almost exactly double.
Good luck .