If you carry an axe, you really dont need a full exposed tang knife.
A full exposed tang knife, is a better survival tool, no doubt. However a stick tang, will better balanced feel lighter, faster in the hand and more responsive. You probably wouldnt notice at first, but after prolonged use when muscle fatigue sets in you would.
You can get hidden tang, partial tang, mortise, tang, rat-tail/stick tang, some are full tang, as in one long peice of steel from tip to tip. Whether its exposed or not its still a full tang.
A full exposed tang, has metal exposed all the way round this can make your hands cold fast.
My personal favourite would be a mortise tang, like the old Ka-bar. Its a 3/4 length hidden handle, very similar to the f1, or the more robust Mora knives.
My favourite handle would be, a full hidden tang, in stacked leather with Stag pommel. Like the Marbles ideal or old Randalls.