The obvious answer would be real is best simply because that is what the fish naturally live in. But as with many things it isn't quite so simple. When small volumes of sea water are collected and stored various changes occur which don't happen when the water is left in the sea itself. These changes make the choice a lot less simple.
Typical forum advice (and this is a direct quote)
"hey let's scoop up some water and ad it to my very expensive and cherished SW tank.. while were at at lets grab some brooklynella, and amyloodinium.. you know what we could use some sand too, grab that stuff with all of the burrowing predatory crabs and burrowing mantis shrimp init, and don't be about that patch with the sand flea and isopods..." it's reckless and completely stupid to think you run NO risk of introducing malevolent into your tank."
Myth 1, Natural sea water is polluted - When asking about using natural sea water on almost any forum the first thing that you are likely to be told about is pollution. But think about it for a moment, if you collect the water from the same area that you collect your livestock is it really going to be polluted so badly, if so why hasn't it harmed the livestock already?
Myth 2, Natural sea water is full of pathogens - There is a small chance that something undesirable could be collected with natural sea water but it is important to keep it in perspective. It is far more likely that a pathogen or a parasite will be introduced through adding livestock to the tank than by adding sea water.
Accidental introduction of livestock - Let's face it, you would have to be some kind of idiot to accidentally introduce a crab to the tank without noticing when only water is being added, and what about live rock I wonder if the person offering this advise has added any live rock to their tank? There is far more risk of introducing an unwelcome guest in to a tank from live rock than from any amount of sea water.
Real sea water - The obvious advantage is that it's free and very widely available if you live near to the shore. But it does have some drawbacks too. It contains less buffers, which mean the pH is likely to be less stable in the long term. You can either make more frequent water changes or use additional buffers to counter this. Real sea water comes premixed, this means it is very heavy (10 lbs per gallon) and it is awkward to transport. At certain times of the year there is likely to be plankton present, this is largely harmless but it is likely to rapidly multiply under aquarium conditions and then crash once the plankton food source has been used up. This in turn could lead to the oxygen level being depleted in the aquarium. To avoid this, store the sea water for a few days in a dark container with a small internal power filter installed. No other pre treatment is really needed. Don't collect water from rock pools, this is because water in rock pools is subject to change, a heavy shower can easily alter the SG as can a hot sunny day, always collect from the sea itself in an area which is away from land drains, river estuaries ect. It's really just a matter of using a little common sense in order to avoid obvious problems.
Real sea water - Cheap but involves a lot more messing about.
Artificial sea water - Expensive but very convenient.
It really depends on your own situation as to which is best. Both have their advantages and disadvantages, if you live very close to the sea and don't mind setting up a few things to correctly collect and store sea water then that is probably best for you. If you live well in-land and don't have the time to collect and treat natural sea water then a tub of dried marine salt is your best option. On a personal note, I prefer to use an artificial mix.
*r/o water = Reverse osmosis water produced from an r/o unit.
**lfs = Local fish store.
***SG = specific gravity, refers to the density of the salt water which in turn is dependent on the amount of salt dissolved in the water and the temperature of the water.