Going through the reviews of the 3 translations on Amazon.com might help you decide although there seems to be little consensus and it seems to be highly dependent in what you value in translations. I copied parts of two reviews below, the last one has the same passage from the three different translations and I think that that might you help to decide.
I've read all three translations of The Tale of Genji. For those who don't know there are three translations so far, by Arthur Waley, Edward Seidensticker and this one by Tyler. All of them have their flaws. Waley's translation is known for being a beautifully written, but very freely translated, so free that he left out several chapters. Where Seidensticker's translation is known for being more accurate but the language is not as beautiful. Of all three I think I prefer Tyler's. In addition to the story, he gives an extensive description of the culture and a listing of the Japanese names of the characters which is very helpful for figuring out the intricate details of rank and social position. This may be a bit too much information for those who don't know very much about Heian culture.
Another one contradicting this one :-)
Having loved both the Arthur Waley and Edward Seidensticker versions of The Tale of Genji as well as the bits and pieces of Murasaki Shikibu's classical Japanese I had hammered through as a graduate student in East Asian studies, I was thrilled to hear that someone had done a "stunning" new translation of this work I and so many other Genji fans regard as one of the greatest "novels" ever written. Fortunately, a friend of mine, who is also a Genji fan, had the foresight to forward me some random passages of the Tyler version before I actually shelled out any money. In comparing these quotes to the Waley and Seidensticker versions I was much surprised to find that the Tyler translation comes up short in almost every regard, and that even Seidensticker's version, engaging as it is, is somewhat disappointing. Compare their respective translations of this short passage from a scene in Chapter Five ("Murasaki"), where Genji is visiting a Buddhist monastery in the mountains:
Genji felt very disconsolate. It had begun to rain; a cold wind blew across the hill, carrying with it the sound of a waterfall--audible till then as a gentle intermittent plashing, but now a mighty roar; and with it, somnolently rising and falling, mingled the monotonous chanting of the scriptures. Even the most unimpressionable nature would have been plunged into melancholy by such surroundings. How much the more so Prince Genji, as he lay sleepless on his bed, continually planning and counter-planning.
Genji was not feeling well. A shower passed on a chilly mountain wind, and the sound of the waterfall was higher. Intermittently came a rather sleepy voice, solemn and somehow ominous, reading a sacred text. The most insensitive of men would have been aroused by the scene. Genji was unable to sleep.
Genji felt quite unwell, and besides, it was now raining a little, a cold mountain wind had set in to blow, and the pool beneath the waterfall had risen until the roar was louder than before. The eerie swelling and dying of somnolent voices chanting the scriptures could hardly fail in such a setting to move the most casual visitor. No wonder Genji, who had so much to ponder, could not sleep.