I'm not entirely sure of what to make of the two scenarios you asked about, but I think what you are asking is whether it yields better performance to reproject your data on the fly in a map service as opposed to reproject your data ahead of time and subsequently publish it so that it doesn't have to be reprojected on the fly. Here are the two scenarios that I am taking away from what I think your question might be:
Scenario 1: Your data currently resides in Projected Coordinate System (PCS) "A" but you want it to display in PCS "B", so you change the data frame in your MXD from "A" to "B" and publish the MXD as a service. While the underlying data exists in "A", it is being rendered in "B".
Scenario 2: You actually perform a one-time, up-front reprojection of all your data using the ArcGIS Desktop tools such that they are modified from PCS "A" to PCS "B". Now they reside in "B". Then, you add the data to an MXD and publish it as a service without modifying the data frame.
Let me know if I am understanding your question or not. Scenario 2 will yield better performance because the data is being published in its native Projected Coordinate System rather than being reprojected on the fly with each request as with Scenario 1.