For '57-60 nailhead 364, both hoses are 1-1/2" on each end.
For '61 nailhead 364, both hoses are 1-1/2" on one end and 1-3/4" on the other end. The cylinder water outlet and water pump did not change from '60 to '61, so the radiator pipes must have increased in size.
The original Buick part numbers are different for every year on both hoses. Could not find the dimensions in any Buick data. The RockAuto site shows replacement hoses and their crossover numbers under ACDelco, Gates, Dayco and others. The Gates recommendations are good about going back and crossing to the original Buick numbers. The 1961 listings get tricky and show some hose id dimensions in 16ths and 8ths instead of the standard 1/4" steps shown elsewhere. Probably both will work.
What has been, can be again. (Bob Wills, 1942)