I did more extensive testing this morning and using the same input dataset I chose the projected coordinate system with Spaces or Underscores (two tests).
Using the same input feature class I PROJECTed the output to NAD 1983 UTM Zone 11N choosing either the 'spaces' version or the 'underscore' version. The resulting output differs in SPHEROID and some subsequent parameters (Details attached).
Output Coordinate System PROJCS["NAD_1983_UTM_Zone_11N",GEOGCS["GCS_North_American_1983",DATUM["D_North_American_1983",SPHEROID["GRS_1980",6378137.0,298.257222101]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["False_Easting",500000.0],PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",-117.0],PARAMETER["Scale_Factor",0.9996],PARAMETER["Latitude_Of_Origin",0.0],UNIT["Meter",1.0]]
Output Coordinate System PROJCS["NAD_1983_UTM_Zone_11N",GEOGCS["GCS_North_American_1983",DATUM["D_North_American_1983",SPHEROID["Geodetic_Reference_System_of_1980",6378137.0,298.2572221008916]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["false_easting",1640416.66666667],PARAMETER["false_northing",0.0],PARAMETER["central_meridian",-117.0],PARAMETER["scale_factor",0.9996],PARAMETER["latitude_of_origin",0.0],UNIT["Foot_US",0.3048006096012192]]