Steve,
When the fit is good and the wood surface area is sufficient, for smaller airplanes the CA is fine. I have never had one come loose. I align the stab and then tack it in place with thin. Then I angle the fuse and run the thin so it wicks well into the joint. If there are a few small gaps I will run a neat bead of medium or thick along each side. Just like Star Wars, do not under estimate the powers of the Dark Side, er, CA.

On the Flip, CA will work just fine.

Regards,
Mark