It makes sense that the version popular in Is-Ra-El was the one that referred to God as Elohim.
The Elohist texts represent a conception of God that was closer to Atenism, with God as an abstraction, and with angels necessarily mediating between this world and the next.
Favored Moses over Aaron.
Talks about Mount Horeb, instead of Mount Sinai. If Horeb was short from Horemheb, it wasn't the mountain of God, but rather, God himself, who was the destination. Hence the texts are acknowledging the supremacy of the pharaoh (for whatever reason).