Each system has its ups and downs.
Wii - This is the cheapest of the 3. It's a heckuva lot smaller than the other two, with no overheating issues to date. Being light and compact makes it great for travel. In my personal experience, the only problem I've ever really had with it is that sometimes the network stuff freezes up and it has to be manually shut down (controller is unresponsive). Also, this is just a side note, if you ever take a power surge - even with a surge protector, you have to unplug the Wii completely for about 10 minutes before the power adapter pack is usable. This happened twice in a span of a year.
This console has complete backwards compatibility. Any GameCube game will play, but you will need a GameCube controller.
Also, there is a great selection of games. Many use movement and adapaters to utilize the great feature. And for some games, if you don't want to use the Wii-mote and nunchuk, you can easily use a GameCube controller (Wireless Wave Bird for the win). This is the best system for parties, get togethers, family events.
The online play for this console is pretty decent. I wasn't too too impressed, but it's free - so I can't complain. I got the internet feature back when it was in beta - so it was free. New users can get this feature for $5.00 - not too bad of a deal.
Xbox 360 - This is probably the system I've put the most hours on. The controller is pretty much the same as the prior - with better placement of the Start and Select buttons, and addition of the bumper buttons. I personally like the fact that there are so many color variations of the controller. As far as games go, there's a pretty great selection. However, most of the games are not platform specific.
The original release (beige-ish white) has a serious problem with overheating. So much so, that the warranty for the systems has been increase to a whopping
five years. The problem is that the system runs at 96nm (which is pretty fricken hot) and causes a mini-meltdown. This is the infamous Red Ring of Death. Speaking about the Ring of Death, this system is one of the few that uses the lights to explain the error. Each designation of red (1st and 3rd only, 2nd only, etc) lights means a different problem. Very handy.
The Elite and Halo editions do not have the same overheating problem (so far...) as the original releases. The newly made Premium consoles also have the new chipset that runs a lot cooler than the original original.
This console has some backwards compatibility. Most of the more popular titles will play - but sadly, my Phantasy Star Online won't.
As far as online capacity, Microsoft has been testing downloadable content since the original Xbox. Every game released for the 360 has downloadable content. New levels, new characters, backgrounds, etc. Some things are free and some cost money. Demos, for instance, are free. However, if you want to play games online, you have to have a Microsoft Gold Subscription - which costs money.
PS3 - First, I want to make sure that everyone knows that not releases of the PS3 are backwards compatible for PS2 and PSX games. The 40GB is not backwards compatible at ALL. I've got the one that will play all Playstation titles. This is awesome for me starting up Final Fantasy VII again here soon.
This is the most expensive of the Next Gen systems. Some models have a problem with overheating - a simple Intercooler is all that is necessary if yours does. ((Hurray, mine didn't need one)).
The game selection is so-so if you only look at PS3 specific games. These games also have downloadable content - including UserMade content! This is the only system to have attempted this. I only recently got my PS3 (which has been using the preloaded Fold@home) and haven't played it at all. My husband claims that PSX games run a lot more smoothly than they did on the PSX or PS2.
The current PS3 controller makes me a little iffy. Because of contract issues, there is no dual shock in them. So, the controller is light as air! I feel like it's going to crumble in my hands. What's interesting in the Gyro System that recognizes movement. This feature is used in various games.
Also, there is free internets.
All Systems - All of the systems have wireless controllers that are factory made. The 360 and PS3 both have plug and charge packs that allow the user to plug the controller into the game system to charge the battery pack. Very nifty.