Just finished watching this show from the start to the current episode. Much to my surprise I like it a lot more than BBC's Sherlock. Obviously the difference in format plays a great part (20ish episodes seasons allow for better character development than seasons that span 3 episodes), but the BBC show also tries too hard to be clever and stylish and too often fails on both accounts. The comedy is better on the BBC show though, helped by the timing and delivery of Freeman's Watson and the acerbic wit of Cumberbatch's Holmes. Still, Miller's over the top Holmes is very entertaining and with a surprising range and Liu's Watson works very well (and it's not insulting Freeman than saying I prefer seeing Liu on screen! - Is there a wardrobe Emmy?).
Irene Adler and Mycroft are strong on both shows, but Elementary's take on Moriarty is a lot stronger than the BBC's.