I have GPS data that has been recorded in Datum WGS84. The client has a GIS built in Datum NAD27. Having looked into the conversions online I would like to know how to do this rigorously with minimum loss of accuracy. Ordinarily I would build a GIS in WGS84 that uses GPS data and project it to the desired UTM (16N in this case). I know I can transform in ArcGIS 10 but is this rigorous enough?
Some information that would have been helpful if you provided: which ArcGIS version do you have? What accuracy is the customer looking for? What location does the data represent?
You might try a few different paths of transformations. I'm going to assume the data is within the contiguous 48 states of the US and a relatively recent version of ArcGIS 10.1.
You can try a single step, file-based transformation, NAD_1927_To_WGS_1984_79_CONUS. This uses the same conus grid file as the NADCON software.
Because the GPS units are all recreational (or mapping) grade receivers, this more complicated workflow may not really improve results. Use a three step transformation: WGS_1984_(ITRF00)_To_NAD_1983_HARN, NAD_1983_To_HARN_(insert appropriate state/region abbreviation here) and finally, NAD_1927_To_NAD_1983_NADCON.