That depends on what you are looking to do in tax.
If you want to join the Big Four, one of the second tier firms, or the stronger regional practices, that would be more competitive. Having an MST helps but is not an absolute necessity, from my experience. In fact, if you are able to get your foot in the door for interview with the right resume and you have the right aptitude, you do not even need to have an accounting degree, although you will have a steeper learning curve and will need to make up for the licensing requirements to rise through the ranks.
You should be aware of the campus recruitment efforts of the accounting firms at different campuses and take that into account when you select your school, IMHO. It is important to secure internship positions during your studies, so that you can familiarize yourself with your prospective employer's system, make good impressions with your performance, and secure an offer in the final year.
On the other hand, if you want to be a competent tax professional and joining a more sizable practice is not one of your ambitions, you may consider starting with a local practice provided you can find one with a good mentor (which will be important) and focus on passing your EA exam.
There are pros and cons with joining larger and smaller firms. With larger firms, you tend to specialize in a certain area, have better access to training and resources, and, with proven capability, get good exposure to big consulting projects as well as more opportunities for local/regional/national/international rotation. There is a price to pay though, which is the hours you clock in. With smaller firms, you tend to deal with a wide variety of tax returns and that could make your experience more relevant to the wider market, especially if you ever strike out on your own.
The bottom line is whether you are looking for depth or breadth in your experience and what your career goal in tax is. Of course, getting more education never hurts. But your priorities will differ depending on what you are aiming for.
Still an AllStar