Neutron mass: 1.008664 u

Proton mass: 1.007276 u

Why the discrepancy?

On a related note, how does one go about measuring the mass of a neutron or proton, anyway?
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A proton is made of two up quarks and a down quark, whereas a neutron is made of two down quarks and an up quark. The quark masses contribute very little of the actual mass of the proton and neutron, which mostly arises from energy associated with the strong interactions among the quarks. Still, they do contribute a small fraction, and the down quark is slightly heavier than the up quark, which approximately accounts for the difference. (The masses of the up and down quarks, because they're so small, are not extremely well-measured, and detailed calculations of what the proton and neutron masses would be for given quark masses are difficult. So it's hard to be quantitative about the answer in a precise way.)

You can read a bit about the state of the art in calculations of the proton mass here: <http://news.sciencemag.org/sciencenow/2008/11/21-02.html>
We can write approximately assuming strong energy $E\_s$ contribution inside proton and neutron is almost the same:

$m\_n c^2 = m\_d c^2 +m\_d c^2 +m\_u c^2 +E\_s $

$m\_p c^2 = m\_u c^2 +m\_u c^2 +m\_d c^2 +E\_s +E\_c $
in terms of quark u and d masses and $E\_c$ - electrostatic energy around and inside the proton, which can be calculated classically $E\_c = \frac{3}{5} \frac{k e^2} {R} = 1 MeV $, and R=0.87 fm is charge radius from scattering experiments.
Thus we have
 $m\_n c^2 -m\_p c^2 $ = $ m\_d c^2 - m\_u c^2 - E\_c $ = 4.8 MeV - 2.3 MeV - 1 MeV= 1.5 MeV

On the other hand we have $m\_n c^2 -m\_p c^2 $ = 1.3 MeV i.e very close (and quark masses are not know so precisely)