The following result is due to Kaplan (Theorems 2 and 3 in the paper quoted below): 

>Let $p<q<r$ be primes, and let $s > q$ be prime such that $s$ is $r$ or $-r$  modulo $pq$. Then the heights of the cyclotomic polynomials of order $pqr$ and $pqs$ are equal. 

Using this result for $p=3$ and $q=5$, the problem in the question is reduced to checking it for a single prime in the relevant classes modulo $15$. 

This seems feasible to do; I may to so later, then honoring with the request for a Yes/No answer.  

<cite cite="_J. Number Theory_ **127** (2007), no. 1, 118--126" mrnumber="2351667" authors="Nathan Kaplan">_Nathan Kaplan_, [**Flat cyclotomic polynomials of order three**](http://dx.doi.org/10.1016/j.jnt.2007.01.008), _J. Number Theory_ **127** (2007), no. 1, 118--126.</cite>