One of the reasons that I am asking this is because I am interested in both transportation planning and urban design, which leads me to a few more questions...
I am wondering how beneficial an urban design concentration would be. Would having one concentration over the other would limit my jobsearch? For example, if I specialize in urban design but take a few transportation planning courses, would I be qualified to take a job in transportation planning? and vice versa?
A MUD is a shorter, more intense post professional degree 1-1.5(ish) year degree, usually meant for after a 5 year architecture/landscape arch professional degree to "broaden their realm", so to speak. It's really not meant for planners unless you finished an MUP and have a new desire to build a design portfolio and work for an design firm. Though it can depend too. In the city where I'm in, CMU's MUD program is now 2 years and resembles a planning degree more than other MUD degrees.
The question is what do you want and what do you think you have the skills for? A Planning degree is much more broad and less technical than a MUD. It's also more flexible and allows a lot of room for electives. MUDs are shorter, tend to have a stricter curriculum and are extremely small (<10 people per cohort, very studio focused).