Overall, yes. As you break the gaming market down into various sections, no, not as much.
To me, the best analogy is trucks versus cars. If you are mostly interested in what a truck can do for you, then you buy a truck. Or perhaps if you can afford it, a truck and a car. Cars can do somewhat the same things as a truck. They can carry a bit of a load, can drive off-road if the terrain isn't too bad, etc. Yet more cars sell than trucks, because they are easier to handle, and do a few things better than trucks do.
Overall, if you are looking at the very big picture, do all of the consoles play video games (do cars and trucks transport people and things?), then yes, then are in direct competition.
If you are looking at the individual market groups, very casual (female, older adults) not that much direct competition, Wii has won that market. Young, close to the same again. Very hardcore goes to X360/PS3, with Wii getting those that after buying one of those, decides to get the Wii as a second console.
Probably the only market that will get the most competition is the current PS2 owners that haven't gone on to buy this generation of consoles. PS3 fanboys would like to believe that they will go on to buy PS3s once that console gets cheap enough. And a lot will. But some who might have decided to stop buying new consoles as they got older, might instead by a Wii. And as the Wii starts getting more and more games (like the PS2 did), with a wider variety to match its wider audience, some of the more casual PS2 owners will splinter off to the Wii versus buying the mostly hardcore only games of the PS3 or X360.
Torturing the numbers. Hear them scream.
