The "essence," eh? What an interesting question! This is my absolute favorite version of the play (which is actually called Romeo + Juliet and stars Leonardo DiCaprio and Claire Danes), but I've never quite considered whether it has the "essence" of Shakespeare's original. Let's explore the evidence together.
In opposition, there's the issue of setting. If you consider the essence of Shakespeare to be rooted in the Elizabethan time period, then you certainly would have trouble here. Shakespeare's plays were meant to be performed live on stage. This presents real problems for a movie to surpass. Further, Shakespeare's play would have been set in Elizabethan times on the stage while this movie is set in (what was then) the present with the "rapier" and the "dagger" both being types of guns. However, I do not think either of these issues get to the heart of what makes Shakespearean plays "universal."
As my first bit of evidence, I must mention the first moments that Romeo and Juliet first set eyes on each other. The view through the aquarium gives the whole love-at-first-sight idea such a magical and even mystical appeal. The entire exchange in the elevator and beyond with the word play of the banter with the "holy palmer's kiss" is done so incredibly well and a perfect rendition of the flirtation between the two. (Although, yes, it's quite ironic that Juliet is dressed as an angel and Romeo as a knight, but it is a costume party, after all.)
Further, I want to mention the awesome scene of Romeo's and Juliet's wedding night which is strewn with billowing sheets and blissful smiles when the two are together consummating their marriage. Juliet's expression and deliverance of the lines when she realizes that she must be pulled away from her love is priceless. This is just one of the ways that I think the true love of the two main characters is truly shown in this version.
In my opinion, the complete desperation of the lovers exhibited in the final scene is unmatched. I find it hard to explain this in words, actually. Everything from the tears streaming down the cheeks of the actors to the wide-eyed and glassy look of Juliet before she takes her own life. The lines are read with such passion, it just takes my breath away. Then there is the setting of the candles and flowers and crosses that bejewel the tomb that add to that same passion. Amazing!
Therefore, if one thinks that the "essence" of Shakespeare's play is truly the actual love of the two main characters, then this is the movie version that fits the bill perfectly. However, if you want to delve into artistic licence (with Queen Mab being drugs and Friar Lawrence being more of a strange botanist and the weird relationships between the mothers and boyfriends) then, yes, one could take issue with this rendition. All in all, though, this is a play about "star-crossed lovers," and it is the adaptation relevant to those lovers that I believe deserves applause.