I've heard of both methods but since I don't have an air compressor I drain water from the system (lines, tanks and water heater), use a bypass valve to bypass the water heat, pump antifreeze through the system (let each faucet run until antifreeze comes out), then pour antifreeze in each "P" trap and toilet. This requires about four gallons of antifreeze. Using the water heater bypass avoids having to fill the water heater with antifreeze (six gallons or more) to get antifreeze throught the hot water lines.
If you have an air compressor, and can control the pressure so as not to over presurize the water lines, you can minimize the amount of antifreeze you use. You would still probably have to drain the water heater and pour antifreeze in each P trap. I don't think you need to get every drop of water out of the lines and tanks using this method. As long as most of the water is out, and any remaining water has plenty of space to expand when freezing, it probably isn't going to be an issue with respect to damage caused by freezing water. Again, I've never used this method so others that have can give you more insight.