Answer
$^{23}$Na provides more information because it contains the mass number, which is the total number of protons and neutrons in the nucleus of the atom. $_{11}$Na merely provides the number of protons in the nucleus, which we already know because we know that the number of protons is also called the atomic number. We already know that the atomic number for sodium (Na) is 11 simply by looking at a periodic table.
Work Step by Step
$^{23}$Na actually gives us the number of neutrons in this particular atom of sodium. Atoms of the same element sometimes do not contain the same number of neutrons; these are called isotopes of the element. These atoms are all considered sodium, so they contain the exact number of protons as one another; however, they differ in the number of neutrons contained in their nuclei.
If we are given the information $^{23}$Na, we have the mass number, which is the number of protons plus neutrons in that particular atom. By subtracting the atomic number of sodium, which is 11, from the mass number, we can find out the number of neutrons in this particular isotope.
When we are given the information $_{11}$Na, we don't learn much information of value. We already know that the atomic number of sodium is 11, so giving the atomic number is not helpful. This piece of information does not give us the number of neutrons, so it is not as helpful as having the mass number.
