Just to expand on the explanations already given, if it turns out to be helpful:
Axes tend to have very narrow
critical threat range, in exchange for larger
critical multipliers (i.e. you crit less often, but when you do, you dish more dmg)
- Handaxes (light): 20/x3
- Battle Axes (heavy): 20/x3
- Dwarven Axes (exotic): 20/x3
- Greataxes (2-handed): 20/x3
A brief comparison with other weapon types:
- Shortsword (light): 19-20/x2
- Longsword (heavy): 19-20/x2
- Bastard Swords (exotic): 19-20/x2
- Greatswords (2-handed): 19-20/x2
Note that 19-20 (10%) is basically double the chance to crit when compared to a weapon that only crits on 20 (5%).
The
Improved Critical feat adds
+1 critical threat range to axes:
→ Critical threat range
Base
> 20: Hand Axes
Feats
> +1 feat bonus: 'Improved Critical: Slashing' (feat)
= 19-20
Why Swashbuckler?
Short answer: it gives a rare and exceptionally large
critical threat range bonus to handaxes
Details: Swashbuckler was one of the earliest revamped heroic trees, and it can be fairly certainly assumed that one of its main goals was to help boost some weapon types to be more competitive with what was, at the time, a very narrow range of weapons that were considered 'viable'
There are a couple of things that make the swashbuckling stance such an amazing option for handaxes (amongst other weapons):
- bonus to critical threat range
- Single Weapon Fighting style
- Swashbuckling grants a +2 competence bonus to critical range to handaxes
- the vast majority of the trees grant a +1 bonus, so +2 is a fantastic bonus per se
- the rare trees that also grant +2 (e.g. Ravager), grant this on tier 5, which clash with a rare/large critical multiplier bonus (further below, under 'Why Handaxes')
- This +2 competence bonus is doubled if you also have the improved critical feat = +4 threat range
- this is very rare indeed, especially with a low requirement of only 3 bard levels and 6 action points spent in one of its class trees
- As a brief comparison point:
- Rogue 'Assassin': also doubles the threat range bonus granted if you have the improved crit feat, but only from +1 to +2, and it's at tier 5 (requires 5 levels rogue, min 32 action points spent, and only works for daggers)
- Monk 'Ninja Spy': though it does NOT require the improved crit feat, it doubles the crit range bonus granted (While you are centered with any weapon other than Handwraps or a Quarterstaff). It's also at tier 5 (requires 5 levels monk, min 32 action points spent, and only works for kamas and shurikens)
→ Critical threat range
Base
> 20: Hand Axes
Feats
> +1 feat bonus: 'Improved Critical: Slashing' (feat)
Heroic enhancements/spells
> +2 competence bonus: Bard's 'Swashbuckling* [C3]' {base bonus}
> +2 competence bonus: Bard's 'Swashbuckling* [C3]' {*doubled bonus if you have the IC feat}
= 15-20
- Swashbuckling requires wielding a buckler or nothing in your offhand, making the Single Weapon Fighting combat style pretty much a requirement.
- One of the key benefits of this combat style is a very large attack speed bonus, and attacking super fast goes very well indeed with a weapon that crits very often
→ Attack speed bonus = +35%
Feats
> -10%: 'Patience'
Combat style bonus
> +30%: 'Greater Single Weapon Fighting' (feat)
Enhancement bonus
> +15%: Gear/ Augment/ Haste spell
- Single Weapon Fighting is strong for a secondary reason: its very high attack speed bonus offsets the attack speed penalty from the feat 'Patience', which seems to be commonly chosen for swash handaxe builds because it increases your critical multiplier bonus even more (as per section below).
Why Handaxes?
Short answer: the combination of the below lets handaxes reach a very strong critical profile (threat + multiplier) =
15-20/
x6
- a strong base value for critical multiplier
- swashbuckling stance for exceptional critical threat range
- trees, such as Dragonlord/Frenzied Berzerker, grant a rare large critical multiplier bonus
Details:
- Dragonlord/Frenzied Berzerker are rare exceptions, granting a +2 critical multiplier bonus
- The vast majority of the trees grant just +1 bonus
→ Critical damage multiplier
Base
> x3: Hand Axes
Heroic enhancements/spells
> +2 competence bonus: Dragon Lord's 'Conqueror [T5]' OR Frenzied Berzerker's 'Focused Wrath [T5]'
Feats
> +1 feat bonus: 'Patience'
= x6
- And ya, there are some pretty cool handaxe options out there

Note:
Though light picks grant the highest base
critical multiplier bonus value available (x4), they only get a +1 threat range from swashbuckling (also doubled by the improved crit feat), so they don't crit as often as handaxes
Add some extra crit multiplier bonuses (e.g. on rolls of 19-20)...
Feats
> +1 on 19-20 rolls: 'Overwhelming Critical'
Epic Destinies
> +1 on 19-20 rolls: Melee + hybrid Epic Destinies @T5
= +2x
... and the multiplier goes up to
x8
And if you crit on a 19-20 while using a special attack such as..
- Fury of the Wild's 'Fast and Furious [T2]'
- +30% Damage / +3 Critical Multiplier
... the multiplier goes up to
x11
That should be it

Hope I haven't gotten anything wrong, and that this helps expand on the answers already given!