I'd say that for low volume, it's close enough that you don't care. For volume, you'll need to be talking to your PCB and assembly houses to make things as easy as possible for them. and they'll give you the answer that suits their manufacturing setup. For small volumes, knocking the last 3 cents off the PCB cost is a waste of effort. However, if you need a round board, you need a round board - a square one won't do, and vice versa. I don't quite understand the question, I guess.
(About the only way I can see it making any real difference is if you got your square board made in a V-grooved panel, in volume - that'd save you the routing time. It's not going to make much difference, though. In low volumes. V-grooving costs more than routing, as there's more setup involved. In high volumes, V-grooving is cheaper.)
What you really don't want to do is to get round PCBs made, and then ask an assembly house to stuff individual round PCBs. You'll need them to be in panels, possibly with tooling holes, fiducials and all the necessary stuff around the edge.