Measuring protein concentration, Bradford vs. Nanodrop?
That depends strongly on your protein and how exact you need this concentration. Both tests (Bradford and the measurement at 280nm) only do an approximation. 

The measurement at 280nm relies on the interaction of aromatic aminoacids with the UV light. If you have a protein with few or no aromatic amino acids, your measurement will be wrong. 

The same is true for the Bradford assay. Here you form a complex between Coomassie Brilliant Blue and unpolar and cationic side chains of the amino acids. This test is more precise, since it includes more possible side chains, but is still dependend on the composition of the protein.

More precise is the BCA assay, since it utilizes the reduction of copper ions by the peptide bond of the protein.
What you could do is run a BCA assay (or at least a Bradford assay) from your sample and measure the same sample on the Nanodrop at 280nm and compare the results.

You can find an overview over the methods here and here.