"I was just hoping to get some first hand knowledge or suggestions. I know it will mount to both rifles (with some gunsmithing of course), but I would like to get some opinions on which rifle it should be."...." I am looking to stay as period accurate as possible."
In that case you should consider reading or researching two of Peter Senich's books, "The Marine Scout-Sniper" and the "The One-Round War".
Re the 1903: During WWII the USMC used a few hundred 1930s era 1903A1 National Match rifles to convert them into sniper rifles with the 8x Unertl scope. The serial number range for these rifles would be in the 1.3 to 1.4M range, generally speaking. They were used from 1943-1945, often in the Pacific, and again used during the Korean War from 1951-1953, after which they were deemed obsolete. I have a replica of this rifle using a 1.27M 1903 and the Hi-Lux 8x scope.
Re the Winchester Model 70: The Model 70 sniper rifles were not used in WWII or the Korean War. (their was one exception in Korea re Capt Brophy w/ a civilan Model 70, but that's an aberration). In 1965 the USMC needed some sniper rifles for Vietnam, so Maj Edward "Jim" Land requested the former USMC rifle team Model 70s that were in storage in Albany GA, and they also located dozens of the old Unertl 8x scopes that had been removed from the old 1903s, and mounted them to the Model 70 during the early part of the Vietnam War. These would all be pre-64 Model 70s, presumably a bunch with 1941 serial numbers, and some with early to mid-1959s serial numbers. Note: A Model 70 is not legal in the CMP vintage sniper matches.
The first picture is what Carlos Hathcock likely used in most of his time in Vietnam (this pic is the Sporter stock wiith 8x Unertl scope). The B&W pics are from Senich's books.
My replica of a USMC M70 sniper is built on a 1956 era M70, currently w/ 10x Lyman Super TargetSpot, but I have a more proper 10x Unertl that I will mount this winter now that I have black (instead of silver) mounts for it.
Again, I recommend reading Peter Senich's book(s) if you want to built a "period correct" sniper of either rifle. I don't think their is a "best platform" re which way to go,as both are classic rifles, but the 1903 option will likely be easier and somewhat less expensive than building up a pre-64 Model 70. Good luck whichever way you go.