This is purely my own perspective on the matter, but for me TMA vs. MMA deals almost entirely on the its teaching philosophy. Physical skill sets evolve depending on society's needs. Obviously the "traditional" techniques of kenjustu are antiquated for most of society, since we are rarely going to encounter someone wielding a sword on the streets.
For me what separates MMA and TMA is the influence of Zen, Taoist, Confucian, and Buddhist teaching philosophies and life philosophies. This mixed with a quasi militaristic structure provide a path to personal enlightenment. This is not to say that one cannot achieve said enlightenment through MMA, but the paths are different one is a "traditional" path while the other is not.
I was always taught that my art is 70% mental and 30% physical, and the longer I practice, the longer I find this to be true. Otherwise, our seniors would have little place in the Dojang.
In my opinion the more modern approach is to incorporate the Zen, Taoist, Confucian, Buddist teaching philosophies and life philosophies into the martial arts. Originally the arts were developed to protect oneself, one's family, one's lord, one's tribe, one's country not to live a life with these philosophies. In feudal Japan as the wars died down somewhat these practices were brought into the martial arts to help round out the human being. Which is how arts changed from warrior arts to more of the "way" (do) of life arts.
And while in the states these teachings (Zen, Taoist etc. etc.) might not be as prevalent as elsewhere (speaking as being part of a martial system or teaching), the arts are now practiced more as a way of life (improving self confidence, character development, goal setting etc. etc.) instead of the defense of one's self, their family, their community etc. etc.