In addition, one of the benefits of using priming sugar is when you have a pipeline going (Kegerator full) and you have one or more kegs of beer just sitting around, and will be sitting around for a while (or at least until you finish a keg off). Then why not add priming sugar and let them do their thing in the meantime? This way, they're already carbonated, and you don't use up your tank in the meantime. (not that co2's expensive or anything, but you have to make an effort to fill up the tank, or force carb by shaking)
The disadvantage of priming sugar is the small amount of yeast that's created. There are two times you may notice it, at the very beginning, when the diptube is sucking up some yeast. (It clears within a few ounces though, so you may just toss the first three ounces and not worry about yeast again unless you're moving the keg around [or if it's a hefe or other yeast saturated beer]). And at the very end when there's next to no beer left and it's draining from the yeast cake, pulling some yeast with it.
So of the three processes, yes, there are advantages with each one, but they're all different and fit all different situations.
If I've just finished the fermentation & settling process and I want the beer *now*, then the obvious winner is force carbonating. Even if this means that the sharp, acidic co2 flavor shows up a bit more. And there's a chance I may overcarbonate, or undercarbonate.
If it's my 7th full keg and it's going to sit around for a month or longer before I ever get to it, then sugar is my winner, since it takes at least 3 weeks for the full process of carbonation, and letting the yeast clean up it's byproducts. Even if that means there's a tiny bit of yeast at the very beginning and very end. It's only a few ounces and I toss that much each time I drain the bev tubing before I pour.
If it's my 3rd keg, and my cooling unit only holds two (or maybe even just one), and I know that it'll be finished in a week or two, then the slow co2 tank carbonation is probably the best balance. Since it's semi-quick, yet will have time to have the co2 bite dissipate, and I'm not likely to overshoot my desired carbonation level. (Also useful when you have multiple air lines).
There's some fuzzy stuff too about natural vs force co2 and the quality of carbonation bubbles, but I'm not touching too far into that debate (though I prefer natural carbonation, because I'm in the opinion of it somehow creating smaller champagne-like co2 bubbles, while force carbing creates larger ones like soda.)
*edit* All three methods will have about the same amount of co2. But for quick force, you may under or overshoot easilly. For long force carb, you will get what you set it for. For sugar, you have to calculate the amount of sugar.
