Advantage is that you are not adding any chemicals to your water, which takes out the guess work as far as dosage. The disadvantage, if it can even be called that, is that you have to have a source of heat(fire, stove, etc.) in order to bring the water to the boiling point. Also we have to remember that this does not remove chemical such as petroleum or pesticides which can be harmful as well.
In a reverse osmosis filter system, your regular water pressure pushes the water through a membrane and additional filters to remove impurities, which are then flushed down the drain. It’s a rigorous filtering process, a GE Reverse Osmosis System filters water three times, for example. Membranes and filters need to be replaced every six months to two years depending on the type of filter and how much water you use.

I've just finished installation of your 5 stage home drinking reverse osmosis system and I have a few suggestions for improvement. It looks like the faucet included in the package is different than the one in the instructions. I like the upgrade, but it would be nice if you included a compatible quick connect adapter. The Quick Connect adapter that was included (pictured on the right) has threading that is too large to fit on the faucet. The packing nut attachment doesn't work well with plastic tubing.
The addition of inorganic coagulants such as aluminum sulfate (or alum) or iron (III) salts such as iron(III) chloride cause several simultaneous chemical and physical interactions on and among the particles. Within seconds, negative charges on the particles are neutralized by inorganic coagulants. Also within seconds, metal hydroxide precipitates of the iron and aluminium ions begin to form. These precipitates combine into larger particles under natural processes such as Brownian motion and through induced mixing which is sometimes referred to as flocculation. Amorphous metal hydroxides are known as "floc". Large, amorphous aluminum and iron (III) hydroxides adsorb and enmesh particles in suspension and facilitate the removal of particles by subsequent processes of sedimentation and filtration.[6]:8.2–8.3