Statistically speaking, Greatswords deal the most average damage over the course of 20 levels than just about any other weapon, making it the superior choice in almost every case. By the way, I see a few people claiming that Falchions are better than Greatswords, but that simply isn't the case, as Falchions increased crit range but reduced base damage is both a blessing and a curse. Against any critical immune monsters, Falchions quickly become much inferior weapons to the Greatsword.
Most of the other fighter builds either suffer from too little damage, like the sword and board, or in the case of the specialty fighters, like those focused on tripping, too little versatility. Going up against a squad of Giants, a Dragon, a Beholder, or any number of other creatures against whom tripping is either too dangerous or not an option, and you quickly see the weakness such specialty fighetrs possess.
Let's face it, offense is the best defense in the D&D system. I think Greatsword users probably suffer less damage than sword and shield users in most campaigns simply because the opponent dies that much faster, leaving them unable to send out another spate of offensive attacks that could very well finish you or your party. This is especially true in the case of monsters or NPCs with special abilities, like Illithids, or Wizards, who can easily devestate entire parties with one bad string of rolls on the PCs part.
Other weapons simply don't have the offensive power on the same balanced scale Greatswords have. Greataxes deal only around .2 less damage than Greatswords on average, but then you have to calcuate in the wasted damage math. In other words, a critical with a Greataxe may deal far in excess what a critical with a Greatsword would deal, but in the vast majority of cases most of the damage is in excess of what is needed. Greatswords offer a happy medium between mass damage and consistency, which is why they will continue to be the prime choice of melee warriors everywhere, for a long time to come.
