Red Falcon is waaay of the mark like always, don't listen to him.
Axe Auto Attack takes 3.6 seconds.
HB takes 3.6 seconds.
Damage formula is pretty simple.
Power*Weapon Damage*Skill Modifier*Bonus Damage/Armor = Damage
This is extremely easy to see it's true. BTW your tooltips are based on the enemy having 2,600 armor so you can plug in the nurmbers and see its true.
Naked Warrior has 916 Power.
Exotic GS Weapon Damage has 995-1100 which means its 995+1100/2=1047.5.
Greatsword Swing has 0.7 Skill Modifier.
Bonus Damage is not reflected in the tooltip.
So, 916*1047.5*0.7/2600=258.3
Tooltips are rounded up.
http://i.imgur.com/Zl32doJ.jpg
So lets take a full berserker warrior with the typical group spec but no traits taken into account atm to keep it more simple.
20/25/0/10/15
Also lets add a Bloodlust Sigil (250 Power) with Omnom Pies (70 Precision) and Master Maintenance Oil (95 Precision)
2410 Power
57.98 Crit %
2.32 Multiplier
Hundred Blades has a .55 Modifier for the multi hits (8 hits) and a 1.1 Modifier for the last hit.
2410*1047.5*.55/2600=534*8(hits)=4272
2410*1047.5*1.1/2600=1068
4272+1068=5340
Now to add Crit% and Crit Multiplier, i will just use the formula i use in my Excel Sheet.
Damage*((Crit%/100)*(Crit Multiplier-1)+1)
5340*((57.98/100)*(2.32-1)+1)=9426
Now for DPS
3.6 Cast Time
9426/3.6=2618
HB is 2,618 DPS (if you could spam it)
Now for Axe.
Skill Modifier
Chop= .75
Double Chop= .8
Triple Chop= .85
Chop
2410*952.5*.75/2600=662
Double Chop
2410*952.5*.8/2600=706*2(hits)=1412
Triple Chop
2410*952.5*.85/2600=750*3(hits)=2250
662+1412+2250=4324
4324*((57.98/100)*(2.32-1)+1)=7633
7633/3.6=2120
Axe #1 is 2120 DPS
Recap
HB = 2,618
Axe #1 = 2,120
Thats 23% more damage in GS favor.
Obviously this isn't fair because you can't spam HB but if you use HB off cooldown and spam #1 in between.
HB + #1 in between = 1971 which is less DPS than Axe #1
Cyclone Axe + #1 in between = 2252 DPS
So Axe does 2252 with #1 and #2
GS does 1971 with #1 and #2
This is all looks like it favors Axe but when you add Forceful GS giving you might on crit which is on average 10 stacks of might = 350 Power than thats when GS pulls ahead of Axe.
Also keep in mind GS is all about using 2-5 and not using #1 as much since its damage sucks (worse than Hammer #1). Whirlwind is the 2nd contributor to GS damage, which you only use when #4 is up to use while running back or #5 is up to get back to your target, but if the target is against the wall GS 1+2+3 attacks of CD's destroys Axe/Mace DPS.
So Forceful GS adds 10 Might on Average, so to keep up some people run what Strife runs (not saying he came up with it or not) and that is a Sigil on your swap weapon so when you swap you gain 3 stacks of might every 10 seconds so you can have 6 stacks up.
So the difference is 4 might stacks usually. Axe/Mace has about 5-6 Vuln more than GS BTW.
All did comes back to my Original Post, GS is slightly better so pick what you want, but you must use a battle swap sigil to gain might to keep up, which is swapping every 5 seconds.