The anastigmat will be a bit softer, the Tessar will be soft wide open but sharpens considerably from f8 on up.
Kent in SD
Not neccesarily. I have a lens marked "Zeiss-Kodak Anastigmat" It's a 7" f:6.3 Tessar. Another marked "13" Eastman Anastigmat" - it's an f:10 Artar type process lens.Scary sharp. Yet another marked "Goerz Double Anastigmat" - we all know what this is.
Unless the OP gives more info. about just which anastigmat he has his question is unanswerable.