The film draws on the considerable talents of Robert Downey Jr, whose Sherlock Holmes is more action hero than nerdy detective in Sherlock Holmes: A Game of Shadows, while Benedict Cumberbatch in the BBC's adaptation - the first episode of the second series is A Scandal in Belgravia - goes for a more cerebral Sherlock. While they look completely different (Downey Jr spends most of the film covered in a combination of dirt and blood and sporting a black eye, while Cumberbatch is meticulously neat and dressed - when he has clothes on), both do have a lot of similarities.
Downey Jr would beat Cumberbatch in a fist fight, but neither of the actors' detectives shy away from physical violence, and both can easily hold their own. Both versions of Sherlock are very, very clever, as per canon, and they both have a sixth sense, although it's shown in different ways. Downey Jr's detective seems to spend a lot of time forseeing how fights will go, while Cumberbatch's Sherlock uses his ability to gather information on the people surrounding him.
There are plenty of differences in the way the main character is depicted in the two adaptations. Cumberbatch's Sherlock is sarcastic and his humour can be cutting and cruel (as Molly says: "You always say such horrible things. Every time. Always."), although some physical comedy is employed during the scenes in a bedsheet in Buckingham Palace. Downey Jr, on the other hand, decides on a more slapdash form of comedy, with his Sherlock shown as drunk, high and dressed as a woman (during which he spends plenty of time looking like he's in a compromising position with Watson). Cumberbatch's Sherlock has other interests (playing the violin, technology) which help inform his detective work, while Downey Jr's whole life revolves around mysteries (and in this film Moriarty).
Downey Jr's Sherlock's vices are out there for all to see, making him a rather transparent character, while Cumberbatch's has a dark past hinted at often (Watson: "Are you sure tonight is a danger night?") but never fully revealed, giving him depth.
When it comes to Sherlock and romance, the programme again takes the lead. Downey Jr clearly has a romantic connection to Irene Adler (more on her later), but he enjoys dressing up as a woman, a very unsubtle way of getting us to question Sherlock's sexuality. Cumberbatch, on the other hand, shows Sherlock as almost asexual. He is completely oblivious to Molly's attraction to him, and shows a remarkable lack of reaction to Irene Adler when she's naked, although he is immensely attracted to her mind. It would have been enough to leave it at that, but the programme shows other characters discussing Sherlock's sexuality, just in case viewers aren't clever enough to deduce themselves that his romantic life is a mystery.
Winner: Benedict Cumberbatch. His Sherlock is more subtle and layered, and therefore far more fascinating than Downey Jr's.
Jude Law vs Martin Freeman - what a choice.
On the one hand you have the suave Law, whose Doctor Watson is happily in love yet indulges all of Sherlock's whims and always, always forgives him. Law's Watson is Hollywood handsome, as befits a film version, but rather inoffensive and mostly in place just to act as the straight guy to Downey Jr's kooky Sherlock.
On the other hand you have Freeman, famous for his turn in The Office. His Watson cares about Sherlock, but has a life of his own and doesn't take any rubbish from Sherlock, calling him out on his cruelties when he needs to.
Winner: Martin Freeman. Jude Law is just bland.
The woman in Sherlock's life, possibly the only woman he has ever cared about, is Irene Adler.
In the film she's played by Rachel McAdams, while Lara Pulver takes on the role for the BBC in A Scandal in Belgravia. Both characterisations show Adler as sassy, sexy and sly, but with Adler as the focus of the BBC's episode, she's better developed there.
The BBC, or rather writer Steven Moffat, has turned Adler into a dominatrix who finds herself drawn to Sherlock romantically, even though she tells Watson she's gay. She has the brains to almost match Sherlock, although he always manages to best her (even if it takes a while). In the television programme the pair's relationship is based on trying to beat each other, and a mutual respect for their cleverness. Both know nothing will ever happen between them, but both want to keep it that way, because getting any closer would destroy them both.
In the film Adler has a more playful relationship with Sherlock, showing equal affection for him as he does her. McAdams disappears pretty soon after the start of the film, having let Moriarty get the better of her after betraying Sherlock. The film's Adler is disappointing, letting men dictate what she does, while the BBC's Adler puts herself first, plays the game, and is fully prepared to accept the consequences of her actions ("Goodbye, Mr Holmes").
Winner: A Scandal in Belgravia. Lara Pulver's Irene Adler kicks arse, in all ways.
There's plenty of action in A Game of Shadows, which would have included car chases had anyone but Sherlock owned a car. There's plenty to make up for the lack of Fast and Furious type chases though, with a great fight sequence in a bar, a huge shoot out on a train, falling buildings and some one-on-one combat between Moriarty and Sherlock.
A Scandal in Belgravia does show Sherlock as more physical than in the first three episodes the BBC showed. Cumberbatch gets to flex his muscles, but his fights all take place indoors, and against CIA agents, and there's never any sense that Sherlock won't win.
Winner: A Game of Shadows.
Sherlock's brother is only slightly less clever than him, and is more integrated in society, with a role in the government. While both the film and the television programme use the basics, their Mycrofts' are very, very, very different.
In A Scandal in Belgravia Mycroft is serious and brooding, often telling Sherlock off and acting like the dull, older brother, which he is in this case. But in the film Stephen Fry lends Mycroft an air of ridiculousness and comedy, and he never fails to get laughs when he appears on screen (especially when he's naked and his modesty is being covered by strategically placed furniture).
Winner: Stephen Fry in A Game of Shadows.
A Scandal in Belgravia is set in London (apart from the odd couple of scenes), with the capital acting almost as another character. We get to see more of the famous 221B Baker Street, where Sherlock lives (his bedroom has a poster of the periodic table on the wall), and the action takes place in some familiar spaces (Buckingham Palace!). Sherlock Holmes is a very British detective, and his surroundings contribute to that part of his identity.
The film take viewers on a journey across Europe, stopping in countries including France and Switzerland, and it's great to see Sherlock being Sherlock outside of London, although it feels a bit alien.
Winner: A Scandal in Belgravia.
And the winner is...the BBC's adaptation. While Sherlock Holmes: A Game of Shadows is a great action movie, that's not what Sherlock is about. The BBC combines action with subtlety and a brilliant storyline, so pips the film to the post. Let's hope the rest of the series is as good.