The most important part of the guitar for tone is the soundboard or top of the guitar which resonates to the vibrations of the strings. The connection between strings and soundboard therefore effects the tone of the instrument. The most favoured design is to anchor the strings at the bridge which is glued to the soundboard.
An alternative is to attach the strings with a tailpiece. This tends to produce a duller tone but is favoured by some makers.
If you use a glued bridge on a mandolin the relative size of the support piece under the bridge is bigger and reduces the resonance of the sound board. Therefore the tailpiece method is more poular for mandolins and fiddles.
With bouzoukis some makers are now using glued on bridges in an attempt to produce a brighter tone.
Re-gluing bridges is a tricky operation. If you visit some of the guitar builder sites there are a number of tips.