I'm sure there are parts of the office / business you each feel passionate about. If those parts are different make the choice to have the person who is most interested in that area decide the best way to organize or systematize it. All the while making sure the other person understands the system.
If there are areas that you both feel you are the best person to make the decision you will have to find a compromise. Talk it out with open minds and realize you are on the same team, with the same objective. It is not a contest. When your office is a well run, efficient place to be you both win. There is often a way to split the project or task that will make you both happy.
I would suggest discussing and making the decisions that are the easiest or most
You can do this! You will find your way!
If you have a sticking point feel free to schedule a Strategy Session with me. I am happy to help you both talk through any issues you can't get to the bottom of on your own.