The major difference these days is that there are tons more people using Facebook than MySpace. If you look at the charts that graph the amount of use each site is getting you will see that Facebook's line goes up and up, while MySpace's line goes down and down. A few year's ago it was a fact that most everyone had a MySpace account. Now, the ball has bounced to Facebook, and this time literally everyone does.
People still have MySpace accounts and use it daily, but Facebook attracts a much broader demographic. During MySpace's heyday they still did not have many baby boomers or elderly people using it. But Facebook has grandmothers and grandfathers, as well as parents, aunts, and uncles on it. This can make Facebook a little more challenging to use because you have to wonder which people are seeing you do things you did not want them to see.
One key difference is that MySpace always had a focus on music, while Facebook remains silent to this day. On MySpace, the cool thing to do was put your favorite song on your profile so that people were greeted with your pre-chosen tune. With Facebook the only thing that makes a noise are the games. Every profile you view will be quiet, so you do not have to worry about whether your speakers are on or if they're on too loud.
Another key difference is the updates. MySpace has recently added a News Feed similar to Facebook's to try and get people to post mundane updates on their daily activities. This was not invented by Facebook, but they made it popular. Before Facebook added their "What's on your mind?" update box, they were neck and neck in the social networking race with MySpace. Once people started using it and getting addicted to reading updates on their friends, the migration from MySpace to Facebook began.
And probably one of the biggest key difference is that MySpace lets you customize your profile page with HTML skins. Facebook does not, and every profile you view will look exactly the same except for the words contained on it. It sounds a little communistic to be in this day and age and the number one social networking site does not let its users express their individuality. But many pages on MySpace are just plain ugly and hard to read, and with Facebook you never have trouble viewing someone's profile, it always looks clean and orderly.
Another key difference is that Facebook is pretty blatant about using your personal information to target their ads to you. They've taken the Google approach to their ads, whereas MySpace relies mostly on general junk banner ads designed for anyone, Facebook's ads will be targeted down to your update on what you ate for breakfast. Scary stuff.