I think IDPA tends to be more "tactical" while IPSC tends to be more "game." IDPA has a lot more strict rules on the equipment you can use to keep it more "realistic" (i.e. realistic self defense scenerio's) whereas IPSC a lot of the times can become more racey (hence coined of the phrase "race gun").
I've only done IDPA, and I've enjoyed it enormously. I'm a bit deterred by IPSC, since it seems a little bit exclusive (you have to have a black badge course to be "in") but my input on the subject is quite limited. I also like that IDPA is more themed around self defense and, I hate to say it, "real world" scenarios, whereas IPSC seems a lot like challenging and unique courses of fire.
3-gun seems a little bit less prevalent, but I've done some IDPA matches that are somewhat 3-gun style. They're a lot of fun, and basically involve transitioning or using just that - 3 guns, a combination of rifle, shotgun, or pistol.
At my club, I've seen some kids doing biathlon too, and I have to say - those kids are hard workers and that looks like a challenging sport.
It is important to remember that "shooting games" are just that - games (I prefer the term "sports" myself). They're not real world training - if you wanted to do that, you should join the military or police. It's also important to remember that while these sports are fun, safety is always the top priority.
