Sword: The role of the sword is mobility/control/condition damage. In the offhand the sword provides a ranged bleed of massive proportions and a block that also applies bleed, this is a theme that will come up again and again, your build is more defined by your offhand more so than your mainhand and is no different from sword. A condition based build will want an offhand sword and massive adrenaline gaining as to get those high condition damage ratios you will need to use the 4 and 5 in conjunction with flurry to get the most out of high condition damage as flurry is dominantly a condition damage attack. Those using shields or axes in their offhand will want to merely dabble in condition damage and mostly build their warriors without it as the 3rd attack on a warriors chain is a very respectable 1.3 power conversion with a high base damage and no bleed. Physical attacking swords will value the sword for its quick closer and its movement control with cripple and adrenaline now being used mostly for its immobilize. Without a recharge rate increase trait the sword also makes a good weapon swap as it will perform nominally no matter what build you use.
Axe: The role of the axe is damage/area of effect and has the highest sustained damage available to the warrior. Of note is that the 2nd chain attack will attack twice and apply the power conversion over 2 attacks so do not be too enamored with its power conversion, this of course also applies to its 3rd chain attack which is 3 attacks. Regardless the axe is quick and powerful and builds featuring a high power score will find this weapon to be give them large output. The axe has two area attacks in cyclone axe and whirling axe and in the offhand can provide mainhand swords or maces with better power scaleing than their mainhands provide. The axe traits Axe Mastery which is 20 in strength provides 10% more critical damage is much weaker than most weapon specialization traits but still provides more output than some non specialized traits. The second specialization sharpend axes can be found in 20 in discipline and provides with double adrenaline per critical which can be useful depending on your adrenaline needs. This provides the theme for the axe, which is damage damage and more damage, it has great power scaling and its traits go well with high precision. The axe suffers in PVP/WvW from lacking mobility and should be complimented by controlling utility skills like bulls charge and bolas.
Greatsword: The role of the greatsword is mobility/burst damage and creating threads about OP warriors. To the uninitiated getting frenzied hundred blades is a cold welcome to guild wars 2, but to those that know the strengths and weakness of the weapon it does not seem as threatening. The real strength of the great sword is the insane mobility that Whirling attack and Rush provides. With 20 in discipline the trait mobile strikes will let rush/whirling attack/bulls charge break immobilize as if it did not happen as they are all movement skills. 20 in arms will get you forceful great sword which gains might on critical hit as well as 20% recharge rate to the great set of skills that the greatsword provides. This also helps with your spear work when you are stuck underwater and faster tsunami slash will make you the king of underwater combat. 20 in strength will provide you with a 10% increase In damage to both your spear and your greatsword and is a great trait in comparison to most specialization traits as 10% damage is stronger than 10% critical or 10% critical damage and also provides better spear work. Greatsword has surprisingly low sustained damage with its chain attack but makes up for it with might stacks and vulnerabilities to set up the real reason for this weapon the deadly hundred blades. With a massive power conversion of up to 5.5 this is probably the hardest hitting attack in the game and can instantly kill someone under the right conditions. New players without knowledge that stun break also applies to knockdowns/fears will be frenzied bulls charged hundo bladed to death and cry foul is it seems unfair how deadly the combination is. Frenzy and endure pain while both stances do not override each other so players worried about the vulnerability of frenzy can use endure pain to protect themselves during this attack. Hundred blades is most deadly at the end of its attack and as it is a channeled skill it is easy enough to move away. Arcing slice has a 150 range (most melee is 130) but does not provide more damage with over 1 bar in adrenaline and only provides longer fury so having a switch with another useful adrenaline attack is suggested. Moldran of Team Paradigm with his hundred blades to eviscerate build is a great starting point if players want to see the power of a well played greatsword warrior.