With stick on transducers (which I've used on guitar, mandolin, fiddle and ukulele) I usually find unacceptable levels of handling noise and feedback. IMHO they are the least desirable amplification option.
A good undersaddle (which I've used on guitar, mandolin and uke) is less prone to feedback and doesn't suffer so badly from handling noise. It's just a matter of installing them right. They are fine, and they are also the standard way of amplifying fretted string instruments. Undersaddle is what you'll find in most electro-acoustic instruments.
BTW, undersaddles and stick-on bugs are both transducers.