What benefits would you have running a three phase service as opposed to running single phase.

A 3 phase service can deliver more power (wattage) at less voltage with smaller gauge conductors, thus saving copper and installation costs are more efficient than a single phase service.

This is more evident when used for larger commercial or industrial equipment. A single phase motor larger than 10 HP is rare, where 3 phase motors can be much larger.

Chosing between either depends on the total load and types of loads that need to be served.

In terms of running costs, which is more expensive

I was just reading some 2 year old question, and they talked about 3phase being rarely seen in ordenary houses. Here in Denmark, we use 3 phase for our tumble-driers dishwashers washing mashines. Its pretty normal to have everywhere here.

So I quess its pretty cost effective.