Relative Advantages/Disadvantages of Interdisciplinary Degree vs Discipline-Specific Degree
The main reasons are pretty obvious, I think.
A narrow field of study will (probably) make you more suitable for employment in that field and less in others.
A wider field of study will (probably) give you more options, but those who have specialized in something will have the upper hand (again, probably) over you it their specialty.
None of that is necessarily true and you can always either broaden your outlook later or specialize further as necessary. So, I suspect that any effect is most important only for your first job.
But it also depends on the individual program. I can imagine one in which the mathematical techniques are pretty generally useful, but also one in which they are not. This might be worth exploring with you proposed advisor.
On a different dimension, an interdisciplinary program might leave you more grounded in applications, where a straight applied math program might (not necessarily) leave you wondering how to actually use what you have learned.