I think that “The Big Red One” is a better movie than “Saving Private Ryan”.
One thing I really appreciate about "Saving Private Ryan" was the attempt to get the details right, which I think influenced later movies. I grew up watching movies from the 50s, 60s and 70s where the "German" tanks were American Patton tanks with German insignia slapped on. If it's a WWII movie, I better be seeing ME 109s, MG 42s, Tigers and Panzer MK IVs - the details matter.
Not all the movies from the 60s were so casual - "The Battle of Britain" stands out with its ME 109s and HE-111s.