In my experience a triad is the hardest poly relationship structure to pull off, why it is often pursued as an intro level thing baffles me. It is seriously hard (and rare). A triad is made up of (at least) 4 relationships. Given persons A, B, and C. Then A and B, A and C, B and C, A and B and C. It is unlikely to have all of those relationships be of equal intensity at all times.
So to answer your question, is it common for one relationship be more intense than another? Yup, happens all the time.
The only way I think this will work (he says humbly) is if you let individual relationships themselves define the shape your constellation takes. Don't try to force things into a triad if the relationships don't support it. Maybe they will evolve to that shape over time, but maybe they won't. Expecting them to fit from the get go is just going to make everyone involved unhappy and feel unseen/heard.
So that leads to a question for you, would your existing partner be OK with the relationship structure being more of a V? With you and your new partner having the stronger connection and She and your new partner having a metamour relationship?
D