Which is a better unit for expressing molar mass, amu or grams/mole?

While the numeric values are the same the units convey different information.

The term amu refers to the unit which is the value of a proton and the value of a neutron in regards to a mass comparison to the standard that carbon - 12 has 6 protons and 6 neutrons.

When the designation for the the mass is ##(grams)/(mol)## the unit refers to the fact that in 1 mole of a substance there is a specific gram amount.

Let us look at an example of Carbon Dioxide - ##CO_2##

The gram mass of of carbon dioxide ##CO_2## can be determined by combining the mass of one carbon atom and 2 oxygen atoms.

C = 1 x 12.01 = 12.01 O = 2 x 15.99 = 31.98

12.01 + 31.98 = 43.99 grams

This value can be designated as ##(grams)/(mol)## meaning that in one mole (##(6.02 x 10^23)## molecules) there would be 43.99 grams of ##CO_2##.

However, if the unit is designated as amu the information informs us that there are 6 protons + 6 neutrons = 12 ma in carbon and 2(8 protons + 8 neutrons) = 32 amu in oxygen for a total of 44 amu in a ##CO_2##.