PhD in finance/econ vs PhD in mathematics
These are incredibly differently fields, and I feel like you should gain a much firmer grasp of these differences before looking into PhD programs in any.  It's also meaningless to consider which field is "harder", since there will be huge variation between different programs within each field, and between how individuals experience those fields.  

Finance and econ USE a lot of math, but they aren't math degrees.  Between these two I would at least recommend econ over finance unless you know for certain that you want to work/research in finance.  Most econ degrees include some work in finance, along side other econ areas, so you can cast a broader net while still learning what interests you.  In my experience the majority of econ PhD programs require no practical experience, and in fact skew very heavily toward theory.  Econ is also not necessarily related to business - there are a lot of specialties under the "economics" umbrella.

Also, I think it's great your goal is to teach (I also like teaching), but your PhD will be very heavily focused on doing original research.  Do you also enjoy this?  Consider that strongly before embarking on this path, because completing your degree will hinge almost entirely on you being able to sustain a multi-year research project, while practically not at all on your ability to teach.