PHost has extra things you can use, but if you want you can play just like you would with normal THost. The only difference in that case that you have to worry about from the client side is the way alliances are setup\offered.
If you are critical about formulas, then there might be some rounding differences, but for most part this game is setup to be very close to THost.
This is my first PHost game as well. After looking over the documentation ... I may never play a THost game again. I'm in love with the fact I can drop exact amounts of MCs onto unowned planets without waiting a turn. That's just with the extended missions ... there are even Command Messages <head explodes>