I'd greatly appreciate some outside perspective!
Sounds to me like it's time to have a good talk about what you each want out of the partnership, and how to improve it for both of you.
You can discuss criticism, and how to handle it when one partner thinks the other one "needs to fix something." There are different ways to approach this, from let's leave it alone for now and ask the teacher at the next lesson, to talking things through and trying things different ways to problems solve together. (Discuss this in general ... at the moment you are the one getting the criticism/blame, but in the future you may see things you wish he would fix. So pick a way to handle it that works both ways.)
Ideally, you want to avoid situations where either person feels attacked, or where either person feels they need to go on the defensive. This is true regardless of who is ahead or behind the other technically. Aim for mutual respect, and for both acting as if you realize you are both on the same team.
You might try both reading the book "Ballroom Dancing is Not for Sissies" as it goes through a lot of partnership and communication issues.
From what you describe, a lot may depend on how open he is to your input, and how open he is to working on communication within the partnership. It also depends on what your other prospects are for partnerships, to some degree. If he's not available as much as you would like, and there is someone else who is a better fit for your schedule and goals, then it may be time to consider a switch. If you think you'd have trouble finding another partner, then working things through with this one likely becomes your best bet.
If you can find the right partner (whether this one or another one), there are some real benefits to longer term partnerships. Making a longer partnership work takes a commitment to good communication and working together.
As for simple vs complex figures, perhaps you can compromise and at least work on both? Maybe have one wall of each routine be simpler figures, or have simpler routines for warmup, or alternate what you work on from one practice to the next, or something like that?
Good luck, let us know how it goes.