The BK2 is really more comparable to the ESEE 5 in that both are .25" thick. The ESEE 4 isn't quite that thick.
As for the warranty goes, ESEE does have a no questions asked warranty, and while KA-BAR doesn't state that theirs is the same or similar, if you check out the Becker sub-forum you will find both Ethan Becker and Tooj (Senior Engineer at KA-BAR) responding to issues all the time. I've never heard of anyone being turned down for service when it comes to a Becker or KA-BAR knife. They've saved me several times, even when I was downright stupid with my mistakes. My point being that while ESEE states that they have a super-guarantee, KA-BAR is no slouch.
The ESEE 4 is quite a bit more expensive than the BK2 if I recall rightly.
The ESEE 4 is likely to be a bit more handy as a belt knife, but the BK2 is an absolute beast.
If money is no object, go with the ESEE 4... you won't be disappointed. But, if you want a sharpened prybar with great ergonomics and an outstanding company behing them, go with the BK2. You won't be disappointed.