Battleaxe vs Battlesword

[Kyo]

Which one is better in what and in which situations?

[Galgana]

The following statements are mostly based on information from the wiki, particularly the pages for Weapons and Clothing.

Proficiency in axe skill is more common for most cultures than proficiency in sword skill. You would have to roll a specialized build to start with a high baseline skill in swords.
According to the ini_skills.txt file under the game's main directory, proficiency in axe is determined by strength and agility attributes. Same goes for sword, plus dexterity on top of those.

A battleaxe will be cheaper to acquire through bartering compared to a battlesword.
Base value on the wiki is 640 vs 1400; these numbers are equivalent to 80 squirrel hides vs 175 squirrel hides.

Battleaxe is lighter at 3.5 lbs compared to battlesword's 8 lbs.
Encumbrance penalty will matter more when you're wearing multiple layers of armor. The lighter you're outfitted, the less fatiguing it will be to maneuver around.

Defense class rating is 2 for both. It's better to counterattack as a defensive maneuver rather than use these weapons to block when fighting against certain other types of weapons. Otherwise, fall back on dodging if that skill is higher than your weapon skill.
Attack class rating is 4 for battleaxe vs 5 for battlesword. That means you'll be outclassing one-handed swords, knives, clubs, and every other type of axe. All spears are in the range of +/- 1 point in attack class compared to the battleaxe.

One-handed penalty is 15% for battleaxe vs 30% for battlesword.
Equipping a 6-pound roundshield with a battleaxe will raise the carry weight penalty on a level similar to the battlesword while gaining a boost in defense when blocking. Penalty can be mitigated if using masterwork-quality gear because of the +10% skill bonus they provide.
With that in mind, shield + battlesword offers less advantage because of the steeper one-handed penalty.
At the cost of movement speed, the different shield modes offer passive protection from MISSILE attacks only, contingent on direction of incoming projectiles based on which arm is equipped.

This next section is about weapon aspect and armor material types.
Use 'F3' or the 'l' command and select an NPC to bring up the list of equipment they're wearing, then target the body parts with whatever weapon aspect is more effective against a particular armor material type.

Both weapons have 5 in blunt aspect.
The effectiveness of blunt attacks is ordered most to least against the following armor material types (see table of Material Defensive Value under the wiki article for Clothing):

• linen = nettle
• birch-bark = generic leather
• woolen
• mail
• generic fur = lamellar
• iron

In general, it's better to resort to blunt aspect when dealing with the metals-based armors.

Edge aspect for battleaxe is 9 vs battlesword's 8.
The effectiveness of edge attacks is ordered most to least against the following armor material types:

• linen = nettle
• birch-bark = woolen
• generic fur = generic leather

Edge aspect is VERY much less effective against mail, lamellar, & iron.

Battleaxe has no point aspect; battlesword has 4 in point.
The effectiveness of point attacks is ordered most to least against the following armor material types:

• linen = nettle = woolen
• birch-bark = generic fur
• generic leather
• lamellar = mail
• iron

To overcome iron armor, you're better off bringing in a powerful bow/crossbow, or one of the cultural spears (northern, kaumolais, or ango).

Another thing to keep in mind is the weapon degradation system (a toggle-able feature introduced in URW v3.19), wherein damage may be sustained TO weapons when blocking or having counterstrikes intercepted based on:

• weapon weight
• material (wood vs iron)
• impact area
• strike velocity
• attack aspect
• force threshold

Besides the first two, these hard-coded properties can be inherited from base objects for modded weapons but cannot be altered in the current state of the modding syntax.
When you have [WEAPON_DAMAGE:YES] in your urw_ini.txt file, you'll want to pay even more attention to what weapon aspect your opponent is attacking with. These are telegraphed with the following attack declaration strings from messages\urw_combat.txt:

• point = stab
• edge = slash
• blunt = swing

[Pet94er]

Shortly:
Axe lighter and +1 damage.
Sword remarkable bonus.

Winner? Pack of dog!
Second place? Long bow and skis.
3rd place? spear and javelins.

Better if you hit first even if lighter but first, following the rule first (shoot) on target usually winning. Enemy can start to bleeding and in this situation if it is 1 vs 1 combat, you want to run away, if he chase you he loosing blood all the time, if he start to treating wounds, you have some time extra to shoot or throw into him.

[Edico]

If you have the skill for battlesword I'd say it's almost always better, but that can be a big if.  Even though edge isn't effective against metal armor, it's pretty uncommon for opponents not to have weak spots where a sword landing is just immense damage.  Eyes are always a possibility, neck is usually one too, and often they have lightly armored spots elsewhere like knees, elbows, hands, arms.

Back to the previous big if though, you have to either roll a specialized character (or easy mode) to be advanced in swords or spend a lot of time training the skill throwing swords around.