Both Romeo and Juliet fall in “love” quickly, but they are presented from very differing perspectives. Romeo falls in and out of love quickly--look at Rosaline. Juliet, however, does not want to marry the man her father has picked. Perhaps while they tried to convince themselves they were in “love” it is really more a matter of convenience for both of them.
So no, people today aren't that different.
The love of Romeo and Juliet differs from adolescent longings and desires today only through its cultural norms. The characters of Romeo and Juliet are steeped in a place and a time: Verona, Italy from hundreds of years ago. There are definite stresses upon family honor and courtly love that are not stressed in our culture today. In those ways, the loves are vastly different. However, the general feeling of steadfast love is part of human nature and currently remains the same. In fact, it is this similarity that has caused Shakespeare's great tragedy to stand the test of time.
Romeo and Juliet had an iconic love, a tragic, star-crossed love affair that has been the bar by which subsequent centuries of lovers have measured their own relationships. Because they were literary creations, Shakespeare was able to develop their love affair in a truly theatrical manner.
Young teenage lovers in contemporary society would probably not be so driven to get married, mainly because marriage has become so devalued. They also have many other ways to keep in touch with each other, thanks to cell phones, email, and other technologies. Most modern young women in developed societies also do not live under the intense supervision that Juliet experienced.
Since the question is 'does the love differ' (between Romeo and Juliet and people today) the answer has to be No. This emotion, feeling, chemical reaction, whatever you like to call it, is still a natural and involuntary human response. Of course the time and place have changed; that goes without saying, but there will always be examples of young love, starcrossed love, tragic love, impossible love, and unfortunate or unplanned love, regardless of the time and place in our history, sad as it may be.
You would probably be better served asking the question in the Romeo and Juliet group, but that's okay I won't nitpick too much.
Try to separate the time and place and just think about the situation between people. Most of Shakespeares works bear a strong relevance to the situations of today; years into the future, and probably for even as long as humans live, his stories will be relevant because they are stories about real people. I'm sure you're familiar with the phrase 'the more things change the more they stay the same'.
More to the point though, no two situations are exactly the same obviously, but the only real difference you could pin down between the play and today are those differences in the time and place. However in asking if it is different from the love between people today, you are leaving a great deal open because there isn't exactly a standard for love today, and even if there was, Romeo and Juliet wasn't exactly the 'standard' for love even then. It would be quite easy to see how a similar situation could play out between two young impetuous lovers in todays world; this can of course be seen in any one of the many modern adaptations of the play if you need an example.
A similar love can really exist in any time with the only difference being the stage against which the drama is set. To really get to the root of your question I think you need to be more specific as to what you mean about love.