Thanks to both of you, but my point was rather that we shouldn't think in terms of number of attacks, but in terms of attack rounds.
One Great Axe attack round is made by one single blow, and it's only fair that this blow does more damage and gets a higher TP return.
One Hand to Hand attack round is made by two blows, TP gain is split in two and the damage does as well, sort of.

You can't compare a single punch to a Great Axe attack, but you surely can compare two punches (a full attack round) to a Great Axe attack (a full attack round).

My point is that while h2h uses 1handed weapon mechanics (STR>att and DEX>acc ratios etc) it is, from a certain point of view, like a two handed weapon. You can't "split" it in two, you can't equip a different h2h offhand.

Wouldn't it be more fair to get a chance to proc on each fist?