On the subject of axes versus swords, in general axes will do higher damage than swords, with no apparent offsetting advantage for swords (except as might happen randomly through luck – see below). So as far as I can see, it's worth going the extra step of turning your iron into steel and making an axe instead of a sword. This goes for two-handed as well as one-handed weapons.
Remember, there is a certain amount of luck involved in crafting weapons; the result isn't necessarily the same each time. For example, my level 7 (Blacksmithing skill 5) Jahan with Lucky Charm 4 (if that matters – it might; I don't know) just smithed two level 7 one-handed Superior Axes. The first inflicts 59-105 damage (after sharpening) and gives a bonus +1 to Maximum Action Points. The second has no AP bonus but inflicts 62-110 damage.
Incidentally, I've noticed that when I get lucky and smith a higher-damage weapon it gets the higher "after sharpening" damage right off the bat, before sharpening (sharpening on the grinding wheel doesn't improve it).
In general, remember to always sharpen your ax or sword (on a grinding wheel) after smithing or otherwise obtaining it. Then you can combine it with an essence for inflicting supplemental elemental damage, a poison potion for inflicting supplemental poison damage, or Joshua's Spice (if you can find any) for inflicting supplemental fire damage.
It's a good idea for your characters to carry weapons of different kinds of supplemental damage because if you run into creatures of a particular element your supplemental damage of the same element will actually heal your opponent instead of inflicting damage on him. So, for example, when you're fighting the pirates and their water creatures in the Black Cove you don't want to use a weapon that inflicts water damage because that will heal your enemies. Switch over to your poison, air, earth, or fire damage weapon instead (or even a weapon with no supplemental damage). Similarly, don't use your fire damage weapon when fighting fiery creatures.