Depends on the setup. Is machine new or 2nd hand, we bought our first Xerox 3rd party and brand new. Was serviced by an independent company as part of the service contract. Never had a problem. We then bought our second machine direct from Xerox and the service was still actually done by the same crowd as the previous machine.
Personally, yes I'd recommend going direct but 3rd party can be fine too but do your research into them first.