| Drogos |
Your example lacks several very important details (are you using Power Attack, abilities that add/subtract accuracy and/or damage, keen/improved critical, etc.). However, between those three weapons, there's such a very little bit of variation between those three weapons that there is basically only flavor reasons to choose any of those three. The only weapon that really skews these is the Falcata, but since it costs a feat to use regularly it has an opportunity cost associated with it. I don't have all the math, but a search of the forums will provide all this information with supporting numbers.
| Chengar Qordath |
Greatsword and greataxe average out to the same damage: greatsword crits more often, greataxe crits harder.
Falchion depends on your static modifiers and if you have anything extending your crit range. If you have improved critical/keen on the weapon, then you only need +20 in static bonuses for the Falchion to begin beating the greatsword and greataxe in average damage.
| ElterAgo |
It is kind of a toss-up.
Most people will chose the falchion to get the common *2 crits.
The greataxe has the swingy *3 d12 damage, but sometimes you will get that and most of the extra is wasted. Less likely to have any 'wasted' damage potential with the falchion.
But honestly, the numbers are so close that it pretty much doesn't matter.
Do you like the mental image of the giant blade? Great sword.
Do you get a charge out of occasionally chopping someone in half by doing 45 more damage than needed? Great axe.
Do you like shouting 'I got another crit!' over and over again? Falchion.
It's really just personal preference.
Charon's Little Helper
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A Greatsword does 0.5 more damage than a Greataxe and is harder to sunder. The other real option to a Greatsword is an Earthbreaker - which is even harder to sunder and does bludgeoning damage.
A Falchion is only useful if you're a half-orc without martial proficiency. The Nodachi does 0.5 more damage and has the Brace ability. (doesn't come up often - but better to have it than not)
At low levels the greatsword/earthbreaker will be superior with 1.5 more dice damage - at high levels the nodachi will be superior except against targets immune to crits. Or if they have Jingasa and/or fortification.
Before keen/improved crit, if the static damage is more than 30, the nodachi is superior, under 30 the greatsword/earthbreaker is.
After keen/improved crit, if the static damage is more than 15, the nodachi is superior, under 15 the greatsword/earthbreaker is. (Not hard
to get by middling levels.)
(In both cases - this is assuming that the target isn't immune or resistant to criticals. In addition, a critical will be more likely to 'overkill' the target - dealing more damage than required to kill. This is a point slightly in favor of the greatsword/earthbreaker.)