I use front kicks mostly as set ups. I almost never use them as power kicks. Use it to keep the distance, or to thwart a coming attack (a cut kick). They are also good to provoke a passive opponents into countering, and setting yourself up for a decent kick.
Axe kicks, I use them a lot. But you can't lead with this one. You have to set it up properly and use it at a time when your opponent isn't fully concentrated. Like at the end of a combo (when he's moving back), or at a time when he is off-balanced. Leading with the axe kick is almost insulting. But as a followup, it can be a KO kick.
I'm a TKD guy, so things may work differently for you.
And BTW, with front kick, just like any other kick, your bodyweight should be going into the kick. You have to open your hips and drive through, with your whole body pushing into the kick. Don't lean backwards unless it's just a fake. If anything, lean forward.