An FYI... you asked about CA and epoxy -- and certainly those are the most popular adhesives around, but I wanted to stress that there are other options.

Personally, edge joining sheet invisibly and tacking things to hold their alignment while I work on them are about the only places that I use CA. Places where I'm joining big things and warping or moisture and chemical infiltration are potential problems (like firewalls and SOME doublers) are the only places I use epoxies.

Other than that I go with yellow wood glue because it doesn't have nasty fumes or cause long range health questions. It's also way less expensive than the other adhesive types and forms joints that are stronger than the surrounding wood. Like epoxies, it doesn't require the precision demanded by CA glue, it retains flexibility after it's cured.

Another option is the relatively new urethane glues (e.g. Gorilla Glue). These seem to be really great adhesives, better than any of the others mentioned for making a secure joint between imperfectly matched parts. On the other hand, they're not cheap and they do carry long term health implications that will still take years to quantify.

Other than that, there's still the solvent type glues that I really don't think are used very much anymore: Ambroid, SIGment, etc. They're said to be way easier to sand than the other types, but that would make sense because they're more brittle than the others.

And I think that's about all of the major types in use at this point.