1.You should definitely just have the argument and decide who is the CEO. Yes, it will be challenging. But understanding who actually makes the final decision about what now will at least let you avoid 100 small arguments. A good CEO will make most of these sorts of decisions in a way that in the end, if they turn out to be bad, you can change course or roll it back. If you can't even agree to
try an experimental idea... good luck.
2. Agree roles, responsibilities and expectations, and areas of ownership. If you have good traction and he is responsible for driving growth in the market, it sounds like he is doing reasonably well and should probably stay in charge of making the final decision on growth for now. But do you guys have targets or growth goals in mind? If you do, and you're hitting them... just take the win and move on. If you're not hitting your growth goals then that should be enough for you guys to agree to try something different, whether that's experimenting with different pricing, marketing, product etc. Either way, having areas of the business that you can both exercise some agency / decision making over will make you both feel better. And combining that with concrete targets will give you an objective yardstick to measure whether the existing strategies are working.