Barbarian-

Your basic perk.  If you use two-handed weapons with any regularity, take this and get all of it.  Story over, move on.

Champion’s Stance-

If you’re lucky, you don’t use power attacks a lot.  That doesn’t matter much, though, because the really nice perks for two-handed weapons here require this perk anyway.  And, with no off-hand, you have no option for dealing with a blocker other than power attacking to break the block, so go ahead and grab this.  It’ll save you a lot of time spent hammering away for no effect, and a lot more time waiting for your stamina to return so you can cut another big chunk out of your target.

Deep Wounds-

This is not as good as another rank of Barbarian.  I will repeat that- this is not as good as another rank of Barbarian.  On average, taking all three ranks of Deep Wounds will still help less than a single rank of Barbarian.  Not that it’s bad, it just isn’t as good as it could be- even not taking into account that it’s a greatsword-only perk.  Found a better axe than your sword?  Too bad.

Limbsplitter-

Also not as good as another rank of Barbarian.  More interesting, though, in that it basically makes all your two-handed axes mildly poisonous, causing bleed damage for a short time after each hit.  Not terrible, but not great.

Skullcrusher-

This does nothing if your opponent is not actually wearing armor.  Trolls don’t care about this, giant spiders don’t care about this, giants don’t care about this- the list of things that don’t care is distressingly large.  Fortunately, the enemies that do care about this tend to care a lot about it.  Might be worth taking and having a warhammer on hand at all times.