A compression fitting uses a ferrule that bites into the tube. The one big advantage is that there is no special end treatment required to prepare the tube. The installation is a permanent one because once the nut is locked down and the compression fitting sinched in, the ferrule will need to be cut off the tube. The installation is pretty easy to do, but a lot of people don't know the proper methodology. I personally have had leak issues using them in outdoor situations. Swagelok fittings are a very widely used brand of compression fittings and valves. Many places insist on using these fittings.
Personally, I prefer 37 degree flared fittings. I have had better luck with them in leak prevention, especially over long time periods and systems that fluctuate its pressure over wide range. The fittings are a bit less expensive as well. They do require a flaring tool and a bit of talent to make a burr free flare. Some tubing does not flare very well too. Therefore you need to know some special tricks to make them work well (like putting some oil on the flaring tool).