Maggiegrace - You describe my current gaming situation perfectly. I too own a Xbox 360 (bought in 2005) and a Wii (bought in early 2008). I love them both because while still video game systems, they are still quite different from each other.
I have a 5 year old daughter and she loves both systems. Right now, she actually PLAYS the Wii more than I do. But she loves to WATCH me play the 360 and all the extras that the 360 can do.
I am a big video gamer (although my time in front of a system is really only a few hours a week), so please excuse me upfront if I get too long winded in my response.
I have had the Xbox 360 longer so my game library is bigger than my Wii software library, but I have been careful to choose good games for both. There are a bunch of great games for both systems, but there are also some junk games for both. I have noticed that as the Wii becomes more and more popular, the Wii market has been flooded by a bunch of below-average games. Just ask a few questions to friends and family about games that you enjoy and good word of mouth will help you find good games.
The Wii is EXTREMELY easy to pick up and play. The controls of waving the remote around (if correctly implemented in a game) are very natural. This is the Wiis biggest strength and weakness. The controls can be very fun to wave around, but I find there are times that I just want to PLAY a game, not wave my arms around moving a character.
My recommendations for the Wii that can be fun for you as a parent and your kids could enjoy would be Mario Kart Wii, Boom Blox, de Blob, and Rayman Raving Rabbids(1st one) -a game iself with a bunch of crazy mini-games.
My daughter (being the Disney fan she is) enjoys Disney Princess Enchanted Enchanted Journey (adventure game)and Hannah Montana: Spotlight World Tour (music rhythm game). Both of these games I got cheap during Black Friday/Cyber Monday deals.
The Xbox 360 is a different system altogether. Like Master Yoda has said, if you take advantage of an HDTV, this thing is gorgeous. There are tons of games for the system (it has been on the market since 2005) and the online features for the Xbox 360 are astounding. You can connect the Xbox 360 to the internet to download games, TV shows, and even rent movies. I like to buy classic games from the 80's (Pacman, Galaga, etc) through a service called Xbox Live Arcade. Games on this service can be purchased aprox. in the $5 to $10 range. They are yours to keep after that. My daughter LOVES the Disney show Phineas and Ferb. For a $1 or $2 I can buy individual episodes (commercial free) and they also are mine to keep. You will also find shows like Lost, The Office, 30 Rock, etc that you can buy. You can also rent movies via Netflix service. There are also more geeky things you can do with it, but I've gone on way too long.
You have the best of both worlds in gaming systems. Enjoy! Ask us questions here. There have been some great responses here already. Ask friends and family what they like to play. Games for the parents, games for the kids, etc. :wave: