How does Arthur Conan Doyle present Watson and Holmes as very different people?

Dr. Watson's romantic attachment to Mary Morstan is crucial here. We simply can't imagine, in a million years, that someone as coldly logical and rational as Sherlock Holmes would ever give his heart to a woman the way that Watson does to Mary. Watson is presented to us in The Sign of Four as an unabashed romantic, a man who follows the dictates of his heart. Holmes, on the other hand, is concerned purely and solely with what is logical. And what could be less logical than love?
Because Watson is much less devoted to cold, hard facts than Holmes, he's pretty useless when it comes to solving this particular mystery. But his romanticism does have the advantage that it provides much-needed emotional support to Holmes as he goes about his ace detective work. Holmes may not care to acknowledge the fact, but he needs the loyalty of his friend in much the same way that Watson needs the love of a good woman. The two men may be completely different in so many crucial respects, but they share similar needs, and it's their respective ability to fulfill those needs that makes their relationship such a strong one.

Conan Doyle presents Sherlock Holmes as a person whose main mode of perceiving and understanding the world is logical and factual, whereas Dr. John Watson perceives the world primarily through his emotions. Watson is actuated and motivated by loyalty, friendship, and love, including his love for Mary Morstan, and by loyalty and friendship towards Holmes. Holmes, however, primarily needs the stimulation that puzzles and problem solving provide, which is why he has become a detective. When he does not have a case to occupy his mind, he takes cocaine.
As a doctor, and because he cares about his friend, Watson is appalled at Holmes's cocaine habit, which he fears will harm him. For Holmes, however, mental stimulation is at the heart of what makes life meaningful to him, and if can't get through his work, he gets it through a drug. As he says to Watson:

I abhor the dull routine of existence. I crave for mental exaltation.

Holmes criticizes Watson for adding love and emotion to his stories about Holmes's cases:

Detection is, or ought to be, an exact science, and should be treated in the same cold and unemotional manner.

Watson, however, argues that if love or emotion are part of the story, they should be included. This typifies the difference between the two men: Holmes leads with the head, Watson with the heart.