I'd probably make our main antagonists at least somewhat technologically inferior to the Milky Way colonists - they'll still have space travel and so on, but in a straight-up fight with even numbers, our ships would win every time - 'cause I think the dynamic could be sorta interesting: we'll have the advanced technology, but as a natural consequence of our situation as newcomers, our numbers and resources will be incredibly limited compared to theirs, so we'll have to 'play it smart'.
It'd be a little like the dynamic in Gundam Wing/00. Our mobile suits/ships will be able to beat the pants off theirs, even with a substantial numerical disadvantage, but we'll only have, like, five of them to their hundreds. So we'll have to use our resources and ships extremely sparingly.
Of course, this would lead to even more uncomfortable real-world colonialism parallels... But ultimately, they're either going to tell a sensitive and smart story about colonialism or they're not, and adding one more similarity won't really make that much of a difference.