I used MoneySoft(MS) Payroll software in the past. I loved it— simple, easy, flexible, and user-friendly. The biggest issue I have with MS is its accessibility. It is not a cloud-based software. I do not know about BrightPay, but it also looks like it is also a desktop. I use QuickBooks online (QBS) for accounting. It would be an ideal solution if QuickBooks Payroll is good enough as well.
I have heard some people mentioned KashFlow, Payroo, but have no experience of them.