Glues are separated by strength and are dependent by the application.
White Glue or PVA
White Glue is used for various application within low power rocketry. It is the best glue for children because it washes off easily. It was discovered in Germany by Dr. Fritz Klatte in 1912. It has a weak initial set time and can take up to 24hrs to full cure. It has good use in rocketry for fillets between fins and body tubes, but when applied to heavily, can leave gaps and holes. It is not water proof.
Similar in composition to white glue, but has a stronger initial grip when applied. It too will have gaps when applied too heavily but better adheres to wood and cardboard than its cousin, and like white glue it is not water proof.
CA, Cyanoacrylate, or Super Glue
Good for tacking and use in of harding joints, CA is great for field repairs and attaching fins to bodytubes. It has other uses as well. When absorbed into balsa, it gives this porous wood added strength with little added weight. It has a low sheer strength, so it would not be good to attach fins permanently for HPR. It can also be dangerous to use with Cotton. Too much added to a cotton swab or yarn can actually cause it to combust or catch fire. It is not recommended for use with children and/or use in a small spaces without proper ventilation.
Polyepoxide is a thermosetting epoxide polymer that cures (polymerizes and crosslinks) when mixed with a catalyzing agent or "hardener." There are hundreds of ways that these formulators can modify epoxies—by adding mineral fillers (talc, silica, alumina, etc.), by adding flexibilizers, viscosity reducers, colorants, thickeners, accelerators, adhesion promoters, etc. These modifications are made to reduce costs, to improve performance, and to improve processing convenience. As a result a typical formulator sells dozens or even thousands of formulations—each tailored to the requirements of a particular application or market. So as you can see the epoxy adhesives are better for High Powered Rocketry and for items that need much stronger staying power and flexibility. These are good with almost any material IE: wood, cardboard, carbon fiber, and it can be strengthened greatly with fiberglass tape. Unlike CA, it can be much more flexible and can sustain greater punishment. Like steel, its strength comes from its ability to be flexible.