I could have a good maul and a good axe handy, and I would reach for the axe. On the rare occasion I get an axe stuck, a maul (or sledghammer) is useful for tapping in a wedge just enough to free the axe. I then wriggle the wedge free and go back to splitting with the axe.
I use an axe with minimal flex in the handle. For those unfamiliar with splitting with an axe, I suggest starting out with smaller rounds and working up to larger rounds over time, to allow one's muscles/joints/ligaments/tendons to become conditioned to the impact. No bending at the waist. Bend one's knees instead. Control the axe to drive the head through the round without driving it in to the ground.
Keep the axe sharp.
One might find one prefers one axe for splitting rounds, another for cutting, and yet another for splitting kindling.
Just make sure to use a handle that doesn't waste one's efforts by flexing too much. Many modern fiberglass handles flex too much, waste effort, and make it harder to split wood than they should. Not all fiberglass handles do this, but many do.
Stay safe!