Ugh. Frankly, I hate this comparison.
Romeo and Juliet was a comedy/tragedy to show the foolishness of teenage lust when it is mistaken for love. It was not intended to be taken as a story about the greatest romance of all time.
Twilight is a serious romance novel that portrays two teens (well, a teen and a century-old vampire) in lust and tells us that it's love. It's supposed to be taken as (one of) the greatest romances of all time, and it's got a happy ending for goodness' sake.
I can see how one might draw parallels like Romeo=Edward, Juliet=Bella, and Paris=Jacob. The relationships between the characters was similar. I get that. I also can see how the Capulet vs. Montague deal is similar to the Vampire vs. Shifters thing. I can- kind of- see how the Romeo thinks Juliet's dead! thing = Edward thinks Bella's dead! thing, if one ignores the fact that Juliet meant for Romeo to know she was faking and Bella didn't intend for Edward to find out she threw herself off a cliff.
However, when the overall themes of the two stories are viewed side by side it's obvious that they were written with very different themes in mind. R&J shows the foolishness of teen lust/love; Twilight holds teen lust/love up as an ideal to be striven for.
I also don't get the whole Rosalind=Rosalie/Tanya thing. Romeo was in love with Rosalind and she didn't reciprocate. Edward was in love with neither Rosalie nor Tanya. Rosalie was happy with Emmet; Tanya wasn't particularly lovesick for Edward either as I remember.
Of course, one can hardly blame Meyer for intentionally making these connections with R&J. Most people these days are under the impression that R&J was, in fact, written specifically to be a tragic romance rather than a picture of the foolishness of such romance; it's an easy mistake to make, I suppose. Still, the constant comparison bugs me.