Absolutely not. If anything, it is the other way around.
Statistics is much more applied. I did a statistics degree and became an actuary. It has been a very rewarding and impactful career. I am often quite shocked at the poor data/ statistics skills demonstrated by maths graduates, who (presumably because they are specialised in subjects like topology) are far behind their graduate peers with backgrounds in Psychology or Economics.
My sense is that pure math courses mostly make it easier to do pure math later, and otherwise not make much of a difference. In terms of credentials, I would bet they are mostly equivalent - you can steer your career later through a master or taking jobs in your area of interest.
Statistics seems more robustly useful and transferable no matter what you do later. Statistics degrees also tend to cover the very useful parts of math as well, such as calculus and linear algebra.