The tango DJ's role is too variable for a single, generic description to be of any value. In just the 7-8 places where I dance in my city, we have DJs who fill many different roles:
• House fixtures, brought in because they have well-known preferences and tandas that appeal to that studio or milonga's regulars. They have enough different tandas that any given milonga has time for only 30-40% of the total . . . but attend for a month or two and you'll eventually hear it all, twice. Their role is brand recognition and marketing for the milonga: "Come to Place X because DJ Q plays A, B, C, and D, which is the soundtrack of our social club!"
• People brought in for their charisma and/or dance skills. They, too, represent marketing, but the USP is different: "Come to Place X because DJ Q is a pleasant (and good-looking, and well-dressed, and popular, and . . .) person who will talk with and maybe even dance with you!" They announce tandas loudly, throw their hands in the air, and run the milonga like a nightclub. Many such DJs are knob-twiddlers with only the average dancer's knowledge of tango music . . . yet the regulars happily overlook that, while visitors from away come to party with the cool friend they met at a festival.
• Technophiles with all the gizmos and gadgets. They arrive with an expensive computer optimized for deejaying, their own sound board and cables, and gear like their own speakers, a projector to display the current and upcoming tandas, and lighting systems. They may or may not know the music, but they know how to optimize the acoustics and often the lighting of the room for an engaging evening. These people are relatively rare because few milongas here let DJs plug in anything but a computer – usually, you have to use the studio's board, speakers, lights, etc. But where they do show up, they have a following like the previous category, because "puts on a good, high-tech show" seems to have as much marketing pull as "cool and fun."
• Tango musicologists and/or musicographers who know the music in breadth and depth – they can tell you what year this version was recorded in, who arranged it, who is playing each instrument, and often weird stuff like what kind of recording apparatus was used and how many records were cut. A lot of them fall into the traps of playing unrecognizable deep cuts that should've stayed forgotten (because they're undanceable), and trying to "teach" dancers the music (frowned upon here). They have small fan clubs of connoisseurs, so they have some marketing power, but drastically less than the three previous categories . . . the "happens outside the milonga" stuff like amassing libraries, fiddling with tracks, and knowing the history of tango and/or its music has almost no appeal to the vast majority of our dancers, and organizers know this and hire appropriately.
• Fallbacks who don't cost much or anything at all. The studio or event is a "cultural nonprofit" or doesn't have much money, and so the owner or owner's friend, a member of the board or collective, or even a regular dancer who volunteers is all the DJ they can afford. This person is present purely to ensure that music is played as cheaply as possible. They might eventually develop more advanced DJ skills if they do it often enough, but I've encountered few who can't plug a computer into a sound board, who mix Tanturi with Di Angeles or vals with milonga in the same tanda, who forget cortinas, etc.
There are also rarer outlier categories, like DJs who bring people in because they're new or from away or back from away, and dancers are curious, and DJs who trade on having worked in prestigious venues or at prestigious events, which appeals to a certain kind of tango snob.
And then there's every possible mixture of the above. I know of one house fixture who is subversively a musicologist, one charismatic DJ who is not-so-subversively a musicologist, a house fixture who is also charismatic and the place's fallback, a technophile who trades on prestigious past gigs, a fallback who is a not-so-great musicologist, and many others.
However, what consistently matters is marketing pull – how many dancers that DJ's name can bring in – which is entirely a function of what most of the dancers in the area find important at milongas. In my city, that's overwhelmingly "consistent tandas played by a popular person," not "curated tandas played over a good sound system by a knowledgeable person." The audiophile-dancer intersection is a very small, very lonely set here. If there's a second-place concern after marketing pull, it's the other side of profitability: low cost. House-fixture and especially fallback DJs cost less, the former because charging a low price is usually how you become a house fixture, the latter because they're usually not paid at all.
All of this is in the context of regular weekly milongas. Balls, encuentros, festivals, marathons, and live music events with DJs between sets have completely different needs. But collectively, they account for a tiny percentage of the average dancer's exposure to DJs.