I've got both knives (my BM mini-Griptilian is the drop-point model with thumbstud). They are approximately the same length. The BM has a wider handle and feels more secure in the hand; the EDC's handle is quite thin and more slippery. For my hands (small/medium sized) the BM is easier to open open-handed - the layout is just better. I actually don't open my EDC with one hand because it seems awkward.
If you get a 154CM EDC, this steel is, for practical purposes, equivalent to the BM's 440C.
I like the drop-point blade on the BM, and generally don't like recurves like the EDCs because I don't need any extra challenges for my mediocre sharpening skills. As far as cutting ability goes, I'd say these knives are both fine cutters and basically equivalent.
I like framelocks for their simplicity and strength, but I have several Axis-lock BMs and like these too. For ease of use (opening and unlocking), the Axis is a bit slicker.
These knives are actually equivalent in many ways. The biggest difference is probably appearance. The mini-Griptilian looks more "tactical", while the EDC looks pretty unthreatening.
I actually carry my EDC much more than my mini-Griptilian, but I have a full-size Griptilian (also a drop-point) that I carry every day. If I had to carry a small knife only, I'd probably choose the mini-Griptilian over the EDC, because of the better handle and the Axis lock.
miguel