In my experience, the total registration fees weren't much different in NH than MA, when you factor in the excise/property tax billed by your town later. In NH you have to pay the property tax up front (that's the "mos/mils" variable number on your NH registration). IMHO, NH's way is way smarter - don't want to pay your town taxes? Fine, no registration for you. In MA, they have a whole infrastructure in place to collect the tax after the fact, up to and including sending a sheriff out to collect if you don't pay. Classic Mass...
And when I factor in insurance, my TCO is way lower in NH than it was in MA.
NH offers a non-resident registration (and title) for non-residents who own property in NH (intended for people who leave a car year round at a vacation home, for instance). They definitely don't want you taking the car out of NH (town clerks will tell you the registration isn't valid outside of NH, but I never found anything in the law that explicitly states that).
One thing I've often wondered about, but never tried - if a MA resident (who owns property in NH) legally registers/titles a car in NH, leaves it in NH for 6 months, and then re-registers the car in MA, do they owe MA tax, or did I just find a loophole? It would probably be too complicated if you are financing/leasing.
My delivery plan is to pick up my 3 in tax-free Oregon, drive to CA, take the factory tour, and then drive home on the old Route 66 route (LA->Chicago, then on to NH).