A density functional theory study of the structural and electronic properties and relative stability of fluorinated sp³ silicon nanotubes and their corresponding silicon nanowires built along various crystallographic orientations is presented. The structural stability is found to increase linearly with the fluorine surface coverage and for coverages exceeding 25% the tubular structures are predicted to be more stable than their wire-like counterparts. The bandgaps of the fully fluorinated systems are lower than those of their fully hydrogenated counterparts by up to 0.79 eV for systems having a relatively low silicon molar fraction. As the silicon molar fraction increases these differences appear to reduce. For mixed fluorination and hydrogenation surface decoration schemes the bandgaps usually lie between the values of the fully hydrogenated and fully fluorinated systems. Furthermore, the bandgap values of the silicon nanotubes are found to be more sensitive to the fluorine surface coverage than those of the silicon nanowires. These results indicate that surface functionalization may be used to control the stability of narrow quasi-one-dimensional silicon nanostructures and opens the way towards chemical tailoring of their electronic properties.