I may be able to help on this. I own both brands and have used them exclusively both for hunting and general purpose stuff. That being said I think the bigger bang for the buck is definetly BM knives. First and formost the axis lock is probably one of the best locking systems out there. The relative sharpness of the blades themselves and ease of sharpening has to go to BM. I have owned or own at the present time an AFCK, a 550 Griptilian, and a 710. The AFCK is the only liner lock of the BM's I own. It is the 2nd generation AFCK when they started tapping the screws through the liners. One helluva knife even now. The 550 is what I carry most of the time and the 710 I have used alot in the past for hunting and such.
I have owned at one time or another a Mach1, CQC7A, Commander, and a LaGriffe. I now have a mini Commander. First and foremost the fit and finish on the BM knives far exceeds the EKI's I have owned or currently own. Very few tool marks on the liners or the blades themselves. Ergonomics might be a bit better with the EKI's. Sharpness and general user friendliness go with BM's by a wide margin. A knife is a tool and as such I believe it should perform what it is designed to do with ease and little effort on the user's part. Read that as handle ergonomics(as stated EKI's by a slight margin), blade resharpenablility in the field, taking and edge and holding it, ease of deployment, and pride of ownership. I have found the BM's I have give me all of this. The EKI's I have owned and currently own give me some these things but not on a consistent basis as do the BM's.
When I owned the above mentioned EKI's, the Mach1, Comm, LaGriffe, and CQC7a I put them to a little test. I stuffed an old Carhart with newpspapers and went at it with the knives. I am no martial artist by any stretch but what the heck just cutting up an old coat I figure anyone can do. Well the only one that performed half way decently was the CQC7. Actually if memory serves me correctly I don't think I tested the LaGriffe on the coat. Anyways not to belabor the point but these are supposed to be self defense knives primarily. Least ways that is what everyone says is there primary purpose is. You know they cut meat and are intended for that purpose. Well if you can't cut through a jacket espically where I live in the NYS in the winter well what good are they. Especially if you are getting a knife for that purpose. I used a zytel Magna and one other I can't recall here but the Magna absolutely cut rings around all the EKI's.
I know there a thousands of EKI afficianado's out there and rightly so. I have just never found them to be easy to use for much of anything. They don't open mail well, the don't do well in a hunting situation cause of the chisel grind and I can't get them as sharp as I think they should be, and the wave although a novel idea seems to tear the hell out of my pants pockets and if you are not with your shirt tail out you will rip it. Also you have to careful as to who is behind you when you do deploy the wave. Have I mentioned the BEST commercially made knife out there yet? No well for me it is without adoubt the SERE2K. It is a custom quality liner lock that is a brute with wonderful steel that takes and hold an edge like no tomorrow. I have used this knife literally beating on the back of it to dig arrows out of tree stumps. It has held up more than well. Anyways these opinions in no way reflect the thoughts or sentiments of anybody else on the board except me. Keep'em sharp