Sherlock Holmes duels with himself on television. Two "modern dress" productions are running simultaneously. Each has been successful critically as well as commercially: the English Sherlock and the American Elementary. Both are brilliant. But the American take on the characters created by Sir Arthur Conan Doyle is better. It is more creative, while remaining true to its source.

On the other side of the Pond, as they call it, Benedict Cumberbatch portrays the world's only consulting detective. He is accompanied by Martin Freeman as the doctor lately returned from Afghanistan, unwilling to admit he craves adventure as he blogs about his exploits. Mrs. Hudson (Una Stubbs), the landlady as reliable as she is reliably put-upon, has to be dissuaded from her understandable belief that her lodgers are a gay couple -- although they aren't queer, they arguably aren't conventionally straight.

In the colonies, Jonny Lee Miller plays the individual customarily called the most portrayed on screen ever as a recovering addict with more than a touch of Asperger's Syndrome. He is initially under the care of Lucy Liu as a doctor disgraced by malpractice, retained as a minder. Eventually they become professional partners.

In this variation, Holmes has moved from London to New York City. He establishes early on that he and the distaff Watson (given name Joan) cannot ever be physically involved with one another no matter how intimately their lives become blended. Mrs. Hudson shows up as a transgendered character -- a breakthrough primetime role for transgender performer Candis Cayne.

Miller and Cumberbatch famously worked opposite one another before, alternating as Dr. Victor Frankenstein and his monster for the National Theatre. The staging was available in movie theaters, in an A and a B version depending on who was whom. The Romantic-era horror tale prefigures the choice between Holmeses.

Meanwhile, the two Watsons are more alike than not. In these retellings, they have become the equal of Holmes. They retire the image of the bumbling sidekick (see James Mason chasing around an errant pea on his dinner plate) and even add a bit of contemporary snarkiness to the expected loyalty. Neither Watson can match either Holmes in intellectual insight, but they are equally indispensable. They confirm there cannot be a Holmes without a Watson.

The other characters from the canon of fifty-six stories and four novels appear, as they must to delight the reader turned viewer. The same decision was made to slim down Mycroft Holmes, the older brother who is more intelligent but preternaturally indolent. In England, he remains the behind-the-scenes embodiment of the government. In America, his transformed physique is caused by illness he has overcome, his profession being that of a restaurateur. In each instance, the relationship has been brought from the page to the screen with sibling rivalry verging on the comic.

The original criminal mastermind, Professor James Moriarty, has been tweaked. On BBC, he is the effete suitor of coroner Molly Hooper (Louise Brealey). On CBS, the gender flip of Watson is paralleled with Morarity: James becomes Jaime (Natalie Dormer). She is the effective seductress of Holmes under her cover identity of Irene Adler, the only woman who has meant anything to our hero. (The English Adler is an elegant dominatrix.) Adler could be expected to betray the trust of Holmes, but that she would be revealed to be Moriarty is an imaginative triumph.

The official constabulary is well represented. Lestrade and Gregson are there. They are successful only thanks to Holmes, perhaps slightly less so in the stateside edition where the consulting has a more official status.

A new character has been introduced in Manhattan: Marcus Bell (Jon Michael Hill). The last name alludes to the model for Holmes, Edinburgh doctor Joseph Bell (the lead in an earlier, excellent British production). He is the police officer whom Holmes regards as the best on the force; he happens to be African American.

There are structural differences. The BBC airs a season with only a fraction of the installments that would be shown by an American network: three to twenty-four in this contest. Running to feature-film length, the BBC series displays higher production values. The CBS iteration, later to be developed, was criticized before it had begun as an obvious knock-off. Whatever else might be said of it, there is no mistaking it as its own creation.

The BBC writers are more sophisticated with their references to ACD (Arthur Conan Doyle). They drop inside jokes so casually that they would be missed but for bloggers who help with hints. In the premiere, Holmes and Watson are introduced by their mutual friend Stamford exactly as they had been a century and a quarter earlier. As Holmes then had astonished Watson by diagnosing a family member's alcoholism from the condition of a fancy watch, he does again with the same analysis of the latest smart phone.

Sherlock's three nicotine patches are the equivalent of the three pipes of tobacco he would smoke to solve the most difficult problem. He works out "A Case of Identity" as an aside to the main plot. The ACD story, "The Lost Special," that featured "an amateur reasoner of some celebrity," not expressly identified as Holmes, is incorporated into "The Empty Hearse," itself an adaptation of "The Empty House," in which Holmes comes back from his "Great Hiatus." Even the enthusiasm of those who engaged in the pastime of studying Holmes, either "Holmsians" or "Doyleans" depending on your partisan affiliation, the highest order of whom are the Baker Street Irregulars, are paid homage by the title of the first season finale.

The CBS team has been willing to experiment radically. What might have been a campy disaster, transforming John Watson, an archetype of English virtues, into Joan Watson, a post-modern mixed-race Asian American with freckles, is only the beginning of the effective tinkering. They have not been shabby in their invocations of the Strand magazine case file either. The staged suicide plot from "The Problem of Thor Bridge" opens a mystery. This Holmes has more than a passing interest in bee-keeping. (Nor has the BBC been shy about risk. They turned Holmes into a fraud before killing him off, the former probably being more offensive than the latter, since everyone knows the return is certain while reputation is vulnerable.)

Although Miller as Holmes is more human in his fallibility, he also is less human because of his emotional defectiveness. He has heightened self-awareness about his lack of ability to interact with others according to accepted norms. Miller is shorter than Cumberbatch, exhibiting an expression more wild-eyed than wide-eyed.

Unshaven, nostrils flaring, he is the raw Holmes. His sexual appetite, satisfied with prostitutes, makes him uncouth but still rational. The past substance abuse is the clue to his personality. Losing self control is especially shameful for a mind that depends on discipline.

The greatest objection, painful for any admirer to express, about Sherlock is that he does not deduce as Sherlock did. While a few of the inferences are explicated, at least as persuasively as they ever have been in the lineage from William Gillette to Basil Rathbone to Jeremy Brett, many of them are ridiculous.

Perhaps they must be dismissed as jokes. At the end of the first episode (not the proof-of-concept pilot), "Study in Pink" for example, Holmes instructs Watson that the best Chinese restaurants can be distinguished by the bottom of the doorknob on the front door. (Contributors to internet discussion forums have dutifully, if futilely, hypothesized about how this might be.)

If the premise is to believe, however, this recurring phenomenon is a real failing. The reason is that Sherlock Holmes, to those who discover him on their own, as a literary figure, is meant not to impress but to inspire. He educates Watson, who in turn communicates to those who wish to join them at their 221B Baker Street lodgings.

The thrill is to believe the example could be emulated. It might be possible through self-improvement to glance at a person and see their biography. As Holmes tells Watson, "You know my methods. Apply them."

For that to be so, the concepts in fact must work. If they are a charade, a party trick, then the illusion is just that. To love Holmes is to believe in him. Everything can be explained.

Nevertheless, there has never been such mania for Sherlock Holmes. Sherlock and Elementary are complementary, not competitive. Together, they make this an exhilarating moment for anyone who has wanted to hear a companion cry out, "The game is afoot."