How does galactic war determine difficulty?

A community manager for the game addressed this question on the unofficial subreddit. It turns out to be mainly based on your highest Squad Power from a PvP win (whether in GW or Arenas) and not on Arena Rank:

INRAJ: "Arena Rank, why do we save their highest rank and then pick opponents against it?"
ASD: "We don't. We decided not to use that method a while ago."
INRAJ: "Wait. What?"
ASD: "Yeah, we don't do that anymore. We just use their highest Squad Power now."

[...]

We use your LAST PVP SQUAD WIN so long as that power is greater than the last time you won. So we DO take it from Arena, just not RANK, just Squad Power.

As well, your general experience is factored in:

When new players join the game, they're assigned to a new bucket so they're grouped with other new players. We don't put new players in to a bucket where everyone is already 60--THAT would be unfair.

Enemies also get harder the further you progress in the war:

Galactic War is designed to have stronger opponents at the end, and to encourage the player to get stronger.