These two can't be compared, contrasting them together would be similar to differentiating a phone to a music player.
Fair comparison would be CrystalBrite to Matte screen (a.k.a anti-glare) and LED Backlit to CCFL. Now, CrystalBrite or Matte screen comes either with LED Backlit or CCFL, the latter is going to be obsolete soon.
For starters, CrystalBrite is a marketing term used by Acer, similar to what Sony uses XBRITE, Apple uses Glossy screen, Lenovo uses VibrantView, HP uses BrightView and Toshiba TruBrite. This is a high gloss screen that looks like a mirror and reflects objects in front of it, pretty poor for outdoor computing and business use, most people find it quite annoying. However it displays crisper images, brilliant colors, better viewing angles, and sharp contrast. Such display is typically liked by graphic designers.
On the other hand, Matte screen is preferred by business folks because it usually tends to handle glare better, and that it can be used outdoors. Side effect of the matte finish is a slight blurring, reduced contrast and a narrower viewing angle. Which is better is a matter of environment and personal preference. If the screen is in a room that's generally dark, consider a glossy finish. In a controlled environment it offers a best-case picture. Matte finish is best in mixed light, office environment, outdoor use, travel etc. Most of us use our screens in mixed light where the minor qualitative difference is offset by the anti-reflective benefit.
As for LED Backlit, it gives more detail to the screen in shady parts of the picture, and it also gives more vibrance to the white parts of the picture without losing any of the depths of the blacks, this is called contrast ratio. So LED Backlit display gives you improved contrast ratio as compared to CCFL. Another advantage is that LED Backlit display is slim and consumes less power, i.e. this gives a boost to the battery life of your notebook. Downside is that LED Backlit display is more expensive than standard CCFL.
Hope this helps.