The damage shown is adding in the conditional damage as if you'd get it every time.
The extra 1d4 damage is conditional. You only get it if the target is burning, but the full listed damage includes that 1d4 anyway.
So, for the +1 hand axe, it shows: 1d6 + 1 + stat bonus (3) in main hand = 5-10 --but you don't get the stat bonus in the off hand without two weapon fighting, which is why the damage is lower in the off hand.
Whereas the dragon's grasp is showing: 1d6 + 1d4 + stat bonus (3) in main hand = 5-13. And of course, the damage is lower in the off hand because you don't get the stat bonus.
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it's not always good to just look at the damage. You have to consider that some of the damage bonuses are conditional, like with this weapon. It's not all that often that you'll get the extra 1d4 from already burning targets.