Your billing system is more of a preference really, I prefer modernbill because of how many options it has. You can use it with cPanel/WHM, Plesk, Direct Admin, helm, etc. while with WHMAP I believe is only for cPanel/WHM.
There are both positive and negative's if you choose either one. Like I said earlier, ModernBill has many more options. You can fully automate billing, but it is a pain to set up, and the support isn't really something to brag about either. WHMAP is a lot easier to set up, so if your on a strict schedule or don't feel like using up a lot of time to set up ModernBill, go with this. The support is a lot better as well, they have pretty quick responses.
I believe both have a 30 day trial period, or some type of trial period. Try both of them out to see what you prefer.