Wayne, a tractor gyro has certain safety advantages over a pusher in nose-down crashes. The tractor engine hits the ground first, so its mass dissipates its energy directly against the earth instead of against the occupants.
Stability? Not so much. There is a fallacy out there that a tractor aircraft is more stable because the engine "pulls her out straight," like a kid's wagon pulled by its handle. (We all know that the same wagon, if pushed by its handle, will try to jackknife.) The wagon analogy doesn't hold up, though. The wagon handle is hinged to the wagon, and hence the wagon can either line up with the pull or not. The aircraft's engine OTOH is rigidly mounted, so that engine and aircraft always point the same way, pusher or tractor.
The tractor's fast prop blast impacts the cabin, creating more cabin drag than a pusher of the same design. You must streamline the tractor's cabin fully to minimize this effect. The full streamlining results in a lot of side area that can create slip-roll coupling if not addressed.
A tractor config. is almost mandatory if using aerodynamic controls -- i.e. wings with ailerons for roll control. If the ailerons are full-span, they will be energized by the tractor prop blast and work at low speeds. in contrast, you'll lose aileron at low speeds in a winged pusher gyro.
Both configurations face challenges in tail volume. The fact that a gyro's rotor tilts aft reduces the practical length of the tail boom and the allowable height of the vertical tail surfaces.
All practical machine designs involve tradeoffs.