Either are good knives. The becker is less money, but the grip is pretty fat. You may like that or not. For hard use it is no trouble. If you try to do precision work it tends to be a little cumbersome. I end up choking up high on the blade and using the tip instead of holding it by the handle. They do make the mycarta handles to fit the becker, but they are as high as what an esee would be when added to the price of the knife.
Ontario also makes identical pattern knives to the esee as they used to make them for Randall's Adventure & Training. Personally I favor the 5" rat pattern that used to be called the rat-5. Ontario still calls it the same, esee-5 or something similar for ESEE.
The agency I used to work for paid for several of the rat courses and I have the rat 3,4,5 and 6. Around that time they were all made by ontario. The 3 makes a good utility, small game, precision work and alright big game knife. The 4 makes an okay medium use woods knife and excellent big game knife, still pretty good for precision and alright for small game. The 5 is excellent for hunting, butchering and pretty heavy use, small game is a little awkward but efficient there is still pretty good precision work. The 6 is excellent for heavy use and okay for big game, doable but not so good for small game, not very good for precision work it is pretty awkward to try and control fine detail. For me the 5 was the best compromise for what I use in the Eastern hardwoods. I do carry a 3 daily as a general use knife like most folks would carry a pocket knife though.