I'm a big fan of Nole, so it's hard for me to assess the question with complete objectivity. I'll try.
Per playing style:
Federer is a "quick worker", generates a lot of power with seeming ease (and freakish timing) and never appears to be grinding. He's exceedingly graceful, and plays with a lot of versatility. Although he's my least favorite of The Big 3 (personal preference), I certainly understand his popularity and I enjoy watching him. And, I also find the one-handed backhand to be better to watch - a more graceful shot - especially in the hands of a Federer, Wawrinka. Gasquet, etc.
When I first saw Rafa, his athleticism and enthusiasm practically leaped off the screen. I think - while he's almost the opposite stylistically to Fed - that he almost always brings an air of excitement. And it's not only his speed, strength and grit, but his complete game. He has a beautiful, deadly overhead, hits quality drop shots, has amazing hands at the net, and his high, "hook shot" volley is incredible.
Djokovic's game is more subtle, and relies (perhaps, even more than Rafa's) on intelligent point construction. Though a stunningly fluid athlete, he may not be quite as transcendently graceful as Fed. His game is more for a tennis connoisseur, as he does so many subtle things so well. While he has won a lot of matches in the past by out-dueling Rafa and others and matching power with power, he doesn't seem to have the same sheer power as his two greatest rivals. I agree that he doesn't appear to have the flick-of-the-wrist power of Fed or the fire-breathing speed and power of Rafa. But he wins with intelligence, court-positioning and the unique ability to direct and redirect shots almost anywhere on the court at any time. That said, his speed and flexibility is very unique and great to watch.
Honestly, all three are fun for me to watch...and Murray not as much. Part of Novak's appeal is also how his personality plays out on the court...you really see all the emotions during a day's work. (And off of the court, he may be the most genuine, most intelligent (no doubt), most thoughtful and certainly, the most naturally witty and funny.)