Everyone seems to be forgetting the fact that if you invest your skill points into sword or axe, you WILL get the ability to wield 2 handed weapons with a single hand, meaning you can then carry a shield.
Also, high enough into the Axe skill, you will be able to attack faster with the axe, bringing it on-par with the sword speed (but still slow, if you're using 2 handed weapons, when compared to a 1h weapon.)
While you're stuck with a 2h weapon and fighting animals in the wild, the only trick you need to learn is a backwards dash (double-tapping your backwards movement key). Makes those unblockable attacks easy to avoid. It's all about timing.
Ultimately I think the best idea is to stick with ONE weapon style, considering that they both evolve the same way by level 10 - the only difference is Axes get a faster swing and the ability to wield with one hand, and Swords get the ability to wield Bastard Swords and 2h Swords with one hand (instead of a faster swing).
@Felthor: if you want to go digging around the forums, find the spoilers about where to find Souldrinker's hilt. In the chest that the hilt is in, there's a +5 str/+5 dex amulet. Alternatively, you could just run around looking for 2 ogreroot to eat to increase your str.
Edit:
@RivianWitch: the strongest weapons in the game, so far as I've seen, are sold by the vendor in the Bandit Camp (at least, in terms of sword/axe). I'm at the beginning of chapter 2 and he's selling a 95 dmg warhammer (axe skill). It beats the secret 2 handed sword weapons (Souldrinker/Stormwind) as far as I know, unless those weapons have secret properties - but I doubt this, as I tested them extensively. The only downside to the warhammer is that it's blunt damage, but considering it's a good 10 damage higher than the Berserker axe (which does blade damage), I think it evens out against enemies with blunt armor.