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Both are excellent radios, entirely adequate - and then some - for the vast majority of RC pilots. In some ways, those two are the leading contenders in the industry, and the choice between them comes down to a person's own philosophy. This is my take on the differences, as a Taranis owner (I also used a DX6i for several years before that):
The Taranis is the disruptive technology upstart. Its software capabilities are unmatched, and the community around it is arguably larger and more active than all the others put together. There are countless "how to" videos, innumerable posts... even an online OpenTX "university". If you measure greatness by the traffic in the RCG "Radios" forum, the Taranis trounces everything else by a comfortable margin.
The Tananis hardware is adequate but not spectacular. It is a very good buy for the money, but relatively few people buy the Taranis because of its affordable hardware. Instead, it is OpenTX that is the star of the show, and the real aficionados are all OpenTX buffs.
The initial learning curve with the Taranis is not exactly shallow. Once a person grasps the programming model, things fall into place and many end up preferring the wide-open mixer to the classical prescriptive programming of proprietary transmitter firmware. But - some reading is definitely required. It doesn't just leap out of the box, for most people.
The Spektrum DX6 is a classical proprietary lets-make-it-as-easy-as-possible-for-newcomers transmitter, and a damn good one too. For technophobes who didn't necessarily grow up with computers, it is an excellent choice. Most things "just work", and if they don't there is the option of turning to the vendor for support. (In the Taranis case there is vendor support only for the hardware, and probably only from the more reputable dealers. The firmware support is all online, community-based.)
The 6 channels of the DX6 might potentially be limiting for more complex quads and planes, but they will be enough for a beginner.
In a way, the choice is between ecosystems rather than between transmitters.