I think all three shows are constructed differently.
Law & Order deals with the political and moral aspects of crime and life in New York City. Any characterization takes place gradually over time-they really don't emphasize the character's reactions to the news very much. Only after several episodes do you get a chance to understand the people involved-the show doesn't emphasize it.
Incidentally, heard a radio interview with Paul Sorvino a few years ago, and he said that these actors, including himself, really don't leave to pursue other acting opportunities. "Just about everyone who left was fired", he said. And Sorvino, who has starred on Broadway and made many movies, was probably the best known actor the show ever hired.
SVU seems to deal with the horror and psychological makeup of the people involved in the crime. Not a lot of social/political focus like Law & Order the original. Of course, the nature of sexual crime itself is likely to cut across ethnic and racial barriers anyway. Although Chris Meloni is certaily tough enough, and Mariska Hargitay smart and intellectual enough, somehow the characters don't seem to be that well drawn from episode to episode. Although very good, it seems to me the least of the shows, though if the other two did not exist, I would consider it a great show. Does that make sense?
Criminal Intent is a Genius Detective series that owes it's existence to the greatest detective of all, Sherlock Holmes. Essentially, it is a New York City updating of Holmes. The female partner seems competent enough for her lines, but her role is so subordinate there is little she can do.
One thing that nags me slightly about the show, though, is how such an extreme intellectual got on the New York City police force. Even if went to college first, he still would have had to walk a beat first for several years before making it onto the Detctive Squad.
Unlike Columbo, another notable TV Genius Detective, I cannot imagine D'Onofrio walking a beat. Columbo is essentially a working class kid whose intellectualism arrived in answer to his job's necessities. D'Onofrio just doesn't seem to have any "regular cop" in him at all. It is almost impossible to imagine getting along with the other cops on the job while he worked his way up.
Regardless, it is a fascinating series.