A big componet of this is if you can sharpen what you buy. I've never actually sharpened a tool in the field, but at some point you will have to sharpen a knife, at home or in the field.
Handle size is very important. It has to work for you, the best blade is only as useful as the handle. The ESEE 4 has a thin handle for guys with large paws. The G-10 scales from TKC are great, and thicken it up. You could also make some liners to do the same yourself.
IMO the Bravo-1 is about the same knife, length, height, blade profile are all very similar. The spine thickness, edge, grind, steels, and handle are different of course. The Bravo-1 has a thicker, more rounded and longer handle than the ESEE 4.
The ESEE 5 and 6 have thicker handles than the 4, and the 6 would be a great knife to choose. I own the 5, and would not suggest it for most folks. It's really overbuilt for camp chores, and the BK-2 with some micarta would still be a better choice, unless you thin out the edge of the 5.
Lots of great knives out there to choose from, I love Bark River knives, the convex edge is eaiser to touch up and keep sharp, and they just cut better. I'm not one to twist and pry with those knives, I might do that with my ESEE 5 though. A used Bravo-1 could be had for under your budget, here on the Exchange. Just a thought.