Hi Natasha,
Nitrogen does tend to be more nucleophilic than oxygen assuming that you have the same protonation state.
Here asparagine will not be deprotonated at this pH, and the nucleophilicity of the N will be significantly attenuated by resonance (as the N is more likely to have a partial postive charge than an oxygen in a resonance structure.
In contrast, the aspartate tends to be deprotonated at pH 7, augmenting its nucleophilicity through the build up of excess negative charge, and the resonance structure is less significant which also results in higher nucloephilicity.
This is very similar to the nucleophilic acyl substitution at the end of ChemOchem lecture 4 - carboxylic acids are slightly more reactive than amides, which are the least reactive carboxylic acid derivatives.
I hope this helps!
Katt