Djokovic is the most complete baseliner of the 3. Roger is easily the most versatile all around player and it's not particularly close. In today's game, the former counts for more though, no doubt about it.
What is "today's game" versus "yesterday's game"? Which eras are you comparing? If you are talking about the early 2000s compared to today, I totally disagree with your distinction.
This notion that the game "has changed so much" since the early 2000s is utter nonsense. When I watch highlights from, say, 2005 to 2010, there is hardly any difference from the game today, except that the overall field was better and more talented. I find it funny how people simultaneously argue that the Top 3 are out of their prime but that the game is better or more advanced now. If that's so, how are they still the top 3? And how are they in some ways more dominant than ever?
And how are you defining "versatility"? Is it the combination of serve, approach, and baseline game? If so, fair enough. But outside of Wimbledon/Halle (and maybe Basel) where exactly does Federer win matches with his serve, let alone serve-and-volley? Virtually nowhere. And yes, when he does the serve and volley at Wimbledon, it's pretty. But it's not a go-to play on the tour at large. Djokovic and the other player in the top 3 do plenty of effective volleying when they come to net too.
As for Federer versus the other two, I will grant you that when Federer is clicking and playing at his top level, he is the most offensively dominant. But my opinion of his game has been clouded by the number of matches he has lost because of the 1-handed backhand. It is too much of a hole to look past. And saying that he is as "versatile" as Djokovic is difficult to do when Djokovic has the far better resume on clay and can hit backhands in every direction, at every height, and from various depths with a consistency that Federer cannot. The difference in their backhands is too much to just dismiss Djokovic as less versatile.
Djokovic has won all 9 Masters events and has beaten Nadal at each of the clay Masters events. At this point I think it is very unfair to call him "less versatile" than Federer. What I will grant, however, is that he rarely brings out his best offensive game without it being forced out of him. And that's why he has flopped late in the US Open as much as he has.