Yeah I think this is the biggest rivalry in the NH overall, it's constant whereas the rest seem to peak and trough.
Recent history dictates Irish rivalries more, and I think Argentina are the only team where there's proper dislike going both ways for us. England had a bit of dominance lately and the fixture lost a bit of bite, we need a close and controversial game to get it back. I think the biggest England v Ireland clashes are bigger because they're generally played at a higher level but the match up hasn't reached the heights of the 2013-2017 games lately. The fans all generally get on well too I find, after the Wales game this year I found Welsh fans stuck to themselves far more than English fans generally would. (Certainly the ones I came across but it's admittedly a small sample) Currently I think France and NZ is where most of our energy is going.
Scotland v England might be bigger at the moment, obviously it's the oldest rivalry and there is a hilarious lack of respect between the fans of both sides so now that it's actually a competitive tie blood is boiling a bit.