There are a couple of confused responses to this question.
Vaporizers and humidifiers both put moisture into the air, which eases breathing in dry winter air. The difference is in how they do this. Most humidifiers basically draw air across a wet filter, while vaporizers use a steaming or misting mechanism to spray fine particles of vapor into the air. (Some humidifiers also utilize a cool-misting mechanism, just to confuse us, I'm sure).
Warm steam vaporizers make the air feel most comfortable to breathe when you have a cold, but you must be very careful with the placement of a warm steam vaporizer when children are nearby as the spray can easily scald skin. I have also used a cool mist vaporizer, which had the same effect as far as getting moisture into the air, even if it doesn't feel quite as comfy/cozy as warm steam. Cool mist vaporizers are recommended for children's rooms. You will want to choose one with no more than a 2 gallon and change the water every day. Once a week, wash out the water reservoir and and any "slimy" parts with a mild bleach solution.
I have found that vaporizers can be very difficult to keep clean because calcium builds up on the vaporizing mechanisms. The older they get the more cleaning they tend to require. To clean you will need to soak machine parts in vinegar, so be sure that the model you purchase is easy to take apart for this purpose.
Humidifiers are a good choice if you want to increase the moisture in the air of a larger room or more than 1 room. They tend to be easier to keep clean, that is if you purchase the special bacteria-killing chemicals to add to the water each time you fill. I think humidifiers are a more costly way to go, and a bit cumbersome if you just want to use it occasionally to ease respiratory ailments. Of course, humidifying the air all winter can be a preventative to respiratory problems, so consider carefully which suits your needs best.
One last piece of advice if you do go with a humidifier... I purchased a Hunter humidifier one year, only to have the motor quit within a few months. After a lot of hassle, they replaced it with a brand new model, and the same thing happened again! I would say, avoid the Hunter brand.
Good luck!