The Wii is a lot of fun with groups of people; a majority of the games released for that platform are multiplayer ('Super Smash Bros. Melee', 'WiiSports') and would be able to keep young children entertained. Nintendo usually seems to lean more towards younger children, but there are a few fantastic games available that might appeal to someone older ('Resident Evil 4', 'Splinter Cell: Double Agent').
However, the Xbox360 may be more expensive, but with an added hard-drive (there's no need to get a huge one) it still allows multiplayer and can run plenty of interesting multiplayer games that appeal to all ages, such as the 'Burnout' series of games. 'Splinter Cell' is definitely easier to control on the 360, there is also the 'Halo' trilogy to consider: single-player and multi-player first-person-shooting fun for all.
Multiplayer over an internet connection will require a monthly subscription fee and a connection to your router (the Wii doesn't require any wires), but the quality of multiplayer is great and one can have a lot of fun with people from all over the world, chatting via the microphone headset and playing deathmatch 'Halo 3'.
With the sheer number of titles that cater to any age range, as well as the standard four controller ports for multiplayer and the optional HDD and Xbox LIVE (multiplayer, chat, etc), I would recommend you buy the 360 as a console that everyone will be able to enjoy. Perhaps Microsoft has caught onto the brilliance of remote peripherals and have recently released a couple of titles that involve a camera ('You're in the Movies') and a microphone for 'Lips', which is a karaoke game.
The Wii is certainly not a bad choice; it doesn't require a subscription to play online, the nature of the input devices almost force one to physically grapple with the controls, making it a little more fun, and whether you're swinging the Wiimote back and forth in a game of tennis or it's slotted into a steering wheel that you're turning around like an angry taxi driver, it's a lot of fun. Harmless, childish fun.
It really depends upon whether you'd like to please the younger kids more, or your oldest. Personally, I'd go with the Xbox 360; it'll cater to everyone.