well the compression would be a difference --- the LGW is low compression most of the way thru.. the EGDM adjusts the comp as the distortion goes up like an AC type amp does.....
I have both and I think they are vastly different. I use the LGW mostly for lead work. It's not a tubescreamer but it's in the family tree in my opinion. The EGDM is more of a mildish distortion that is great for straight up rock n roll (rhythm and lead), alt country, southern rock, etc. I just love the way it sounds, rich and full. Probably one of my most used pedals.