Maths vs Engineering Career Prospects (Possible Course Change)

Hi,

I'm a maths student whos just finished 1st year at uni. I have been considering a course change to engineering - this is because of my interest in the sector as a potential career path, and have heard it will be difficult to get into with a maths degree.

I was wondering about what career prospects I would be losing if I was to make the switch? I'm sure I'd be less suited for the super number-heavy roles like quantitative analyst or something, but I don't see myself as being that 'numbers guy' as a career.

So, put simply, what does a maths degree offer that an engineering degree does not?

Mainly super quantitative careers, and also potentially careers that need or use maths which isn't really taught in engineering degrees, such as stats and probability.

But would I be right in saying that these 'super quantitative' careers would be more accessible to someone with an engineering degree, than an engineering related job would be to someone with a maths degree? And therefore, an engineering degree offers greater overall versatility in career options?