I can't do a direct comparison as I still have yet to handle the 730. The Genesis is a well made knife and the clip really sets it apart. I'd take the 730 over it because of the lock mechanism. The axis lock will beat any liner lock out there. Both have similar blade shapes, though the Genesis's blade is a bit longer.
EDI seems to be somewhat of a phantom lately. They're still in business, I received two replacement knives from them last week. But you don't hear anything about them, no news of the Rock Lock or of their fixed blade. I'm excited to see both, but wonder if I ever will
I have never held EDI Genesis but I have BM 730 Ares and I can say certainly - no one liner lock can beat the Axis Lock in strength and reliability. If these matters are essential for you - choose 730. It has comfortable handle and very smooth action (it is smoother than on my BM 710 with Axis Lock, I don't know why). Spear point blade is great for self-defense action and is versatile enough for daily use. Clip positions 730 enough deeply in the pocket - 13 mm only stays above pocket upper edge.
I was turned away from the EDI by a retailer. He demonstrated how weak their lock is by banging the spine with the palm of his hand! I went for the AFCK instead. I have handled the 730 and it's sweet. Absolutely no contest in my book.
BM 730 Ares is a superior knife when it comes to the locking mechansim. The Axis lock is stronger, and more reliable. The EDI Genesis I is slimmer and sits deeper, BUT the liner lock is not as dependable. I sold my EDI Genesis I.
If I have to rely on the knife for ANY kind of situation - I would chose the 730 Ares. You can't go wrong with ANY Benchmade Axis lock knife IMHO.