Is the end result the same? Sometimes the right process gets better end results. Especially if you're a new hire, it's worth considering doing it their way just out of humility.

I feel you believe you are my boss. You are not. Stop telling me how to work. It's tiring. You have your way of doing things, I've got mine, both equally good. Should you have a problem with this, contact the charge or manager. I'm gonna go work now.

This is an extremely aggressive way to speak to someone. It's a little wild that this is what you came up with trying to be neutral and diplomatic. Genuinely makes me question if you're understanding this person and your role correctly.

If you're certain that doing it your way is just as good then I recommend the following message:

Hi [person's name]! I wanted to thank you for your help getting me situated into this new role at [company name]. I really appreciate the difficulties of integrating a new team member, and I want you to know I'm 100% committed to doing good work together.

My personal experience with projects like these involves a work flow that looks more like [x, y, z], and the clients that I've worked for using this process were always happy with the results. The process you showed me where it's [a, b, c] doesn't make as much sense to me, perhaps we can schedule some time to go over why it's more effective doing it [a, b, c] rather than [x, y, z]? Otherwise, just for the sake of completing the project ASAP I would prefer using the way I have more experience with.

Happy to discuss this with you further at anytime and excited about the great things we'll be making together 😁

That's a bullet proof corporate email any manager would take a look at and know you're not the problem.