A longtime admirer of Murasaki Shikibu's exceptional work, I fell in love with Genji first through Arthur Waley's translation, which made this admittedly exotic novel accessible to non-Japanese readers. Curious to know more about the Heian period and culture, I acquired Ivan Morris's tremendously helpful and readable "The World of the Shining Prince." Then I discovered Edward Seidensticker's superb rendering of "The Tale of Genji," and have read and re-read that version with deepening understanding and enjoyment. Seidensticker, while presumably adhering closer to the language of the original (which even modern Japanese find difficult to read), gave us a translation which is perfumed by the sensuous beauty of what must have been a truly refined and special time and place (albeit a very limited one).
Now comes Royall Tyler's superb effort, which comes with myriad and very helpful details: each chapter starts with an explanation of the chapter title, how the section relates to previous chapters and the cast of characters. There are also generous appendices including a chronology of events in the novel and a glossary. Line drawings throughout the two volumes (also present in Seidensticker) provide helpful visual clues as to dress and architecture. Tyler's effort seems even closer to the original language, and thereby lies the problem.
This version unnecessarily burdens the reader with ever-changing nomenclature. Since in the original characters are known by their rank-names, and Tyler (mostly) adheres to this usage, the reader is challenged to keep up with the changes. Put the book down for a day or two and you will feel quite lost for several minutes when you restart. As an aide, the translator does provide footnotes to clue you in, but this just makes things more awkward and tedious. For example, at the start of Chapter 43, "Red Plum Blossom" in Tyler's version: "There was in those days a gentleman known as the Inspector Grand Counselor, the late Chancellor's second son, hence the younger brother of the Intendant of the Watch (1)" This same sentence in Seidensticker reads: "Kobai, the oldest surviving son of the late To no Chujo, was now Lord Inspector." How much more to the point!
To conclude, while Tyler's translation is awesome in its scholarship and abundant detail (including sources of the poetry), it is also much less readable. To my mind, the scholarship gets in the way of the story telling. I found myself longing for my Seidensticker at many turns as I went dutifully through the Tyler. Aside from providing a more continuous flow to the story, I also found that Seidensticker's translation of the many poems in the tale more comprehensible and lyrical.
If you are new to this literary masterpiece, you will find the Waley translation the most accessible. If you get hooked on the work, you will probably want the other two. If you must have only one version, however, go with Seidensticker.