Elementary (2012), based USA and created by Robert Doherty premiered Sep 27, 2012. It takes place in New York, where Holmes (Jonny Lee Miller) is struggling with a heroin addiction with the assistance of Dr. Joan Watson (Lucy Liu), an ex surgeon and a sober companion, whose task, assigned by Holmes' father, it is to live-in with Holmes in order to keep him sober.
Sherlock (2010), based in UK, created by Mark Gatiss and Steven Moffat, premiered Aug 30, 2010. It takes place in New York, and portrays Holmes (Benedict Cumberbatch) relation to his brother Mycroft (Mark Gatiss), as well as his friendship with Dr. John Watson (Martin Freeman), recovering from an injury he has sustained while in military service in Afghanistan (interesting how, more than a hundred years later, Great Britain is still messing around in Afghanistan...)
Modern Sherlock Holmes
Both shows are portraying a modern day Sherlock Holmes, and they are both doing a very nice job making the adaption of the classical detective to present day. While Elementary is planned to run at least 16 episodes (in the first season) of 45 min each, Sherlock has fewer episodes (4 in season 1 and 3 in season 2) lasting 90 minutes.
Of the two, Sherlock seems more true to the original Sherlock Holmes cases, and places characters like Moriarty (Andrew Scott) in a central role, Elementary is more a depiction of the mind and personality of Sherlock Holmes, and less a true-to-the-original-cases-show.
One interesting facet of both shows are a play on sexuality between Holmes and Watson. In the UK-based version the live in relation between Holmes and Watson get quite a few raised eyebrows, and Watson has to state, several times, they aren't gay or anything, while the USA-version has done away with the whole are-they-gay-problem by making Watson into a female.
In my opinion both shows are well worth watching, although Sherlock is a little bit sharper and wittier than Elementary, and given that Sherlock is a bit more true to the original, if I had to chose between the two, (again) I'd watch Sherlock first, then Elementary ;)...