You'd have to analyze the economics of it using costs/effort levels to potential ROI. Unless you discover a rank reason to do so, such as Lawn Mowing is dominated by Lead-gen companies, such as Angie's List and Service Magic, but they are leaving Lawn Maintenance alone, maybe, but then why not just shape your content to rank well for both? If you were working for me, and brought forth this idea, I'd have to ask you to present your case with as much supporting detail as possible. Time-based hunches, such as splitting out content to two distinctly separate sites and waiting for Search to catch up, are still money-based hunches. Can your business afford to lose both? If you'd like more specific input, based on your target service area and demographics, I'd be more than happy to weigh in. Just PM me the info.