I'm going to tell my younger son that his older brother will take over my business one day and not him.
That's surprising. How did you decide that your older son will take over?
Because he's always been the one who succeeded every year, and I felt that it was time for him to take over
Even though it's ultimately your decision on who to take over the family business, it's wrong for you to tell your younger son so far in advance that he isn't the favored one to do so. You should take everyone's feelings into consideration as your older son may not even want to take over the business and it's unfair to lay that expectation on him. Instead of ruling out your younger son, ask both him and his brother what they prefer to do in the future so that their preferences can be respected.
I like this idea, but my older son is a hard worker and my younger son needs to prove himself first.
It doesn't matter who works harder. The point is, they need to decide on their futures not you.