How to make the Romulan War different from the Dominion War? Don't show it.
Have ENT start with the peace treaty and show the personal hardships, struggles and losses the crew faced and how they cope with them in the aftermath. Add to that the reconstruction needed, the newly formed Federation with alien races now having to serve together for the first time ever, the drive to move away from war and conflict towards something greater.
It'd be a far more character-driven series and not so much about cool-looking ships, space battles and catsuits.
That might be a LITTLE extreme.
I don't think you can completely skip over Earth's last great conflict before the founding of the Federation (even though that's exactly they DID do
I think the important theme, however, should be Archer building alliances, both in war and in peace.