RE: Which is stronger?
CA's only real benefit is that it is fast and convenient. Normal CA's are inherently brittle, and therefore the "toughness" of the joint is suspect in many cases. You have to use your smarts when deciding if CA is suitable for what is at hand. It has no solvents so the volume applied is the volume you end up with (almost), except that again it is brittle and fillets are of dubious structural value.
Wood glue can make tremendously strong wood-wood joints, but they must be tight fitting and you have no filleting ability. It does have a solvent so there is shrinkage.
Epoxies have the benefit of curing through an addition reaction, there is no shrinkage to speak of, and the structural properties of epoxy make it suitable for forming fillets. Pure unfilled epoxy systems (most of what we use on models) are inferior to a epoxy adhesives with structural fillers, but again the epoxy itself has enough in terms of physical properties to lend a fair job when used for fillets/filling gaps, being as tough as most substrates we use. The bonds have excellent shear and peel strength to most woods, and because you can form fillets you can greatly reduce the localized stresses at the joint by forming small fillets.
The tensile strength alone (not the only important property) of the cured/dried resins themselves are usually greater than the wood substrates. It is the application and the substrate materials that determine the best choice - it's all about transferring loads without creating high local stress [see CP's comment about being pliable]. But in short, for high stress joints of the kind predominantly used in models, epoxies will give the toughest end job. And they tolerate a wide variety of substrate materials so are excellent for mixed material bonds too.
MJD