If you have gaps, use epoxy. I use West Systems, slower setting stuff, and Z-Poxy 30 minute for the things I want to work on sooner. Both are better quality (harder set, easier to sand after the fact) than home depot dual-tube syringe type jobbies. The foamed up stuff filling the gaps doesn't provide any strength.
I do use polyurethane glues for certain parts of guitarmaking, but use it where it's appropriate. Poly glues foam up, so you need to clamp well to minimize the odds of a glue line. They work best in the presence of a bit of water, so a moist sponge run along the gluing surface helps as well. Where do I use it? Joints that are tight, and that I never, ever want to allow to delaminate. Examples include laminating headblocks and tailblocks for acoustics, laminating headstock veneers (front and back), and it can work well for 'difficult' woods, for example gluing up plates in oily rosewoods. It also works reasonably well for gluing carbon fiber to other wood - I've used it for laminating braces, although I'll be using epoxy for that in future, now that I'm more comfortable working with it - epoxy has a learning curve.
Having said that, often as not I use Titebond original for most of these applications, without reservations. Easy to clean up, no mixing required, and for almost everything 30 minutes of clamp time and 24 hours of 'don't stress the joint' is more than good enough.