Hybrid density functional theory calculations are performed for the first time to compare the stability, structural and electronic properties of monolayers and single-wall nanotubes based on pure Mo(W)S(Se)(2) and mixed (Janus) Mo(W)SSe dichalcogenides. The stability, structural and electronic properties of Mo and W dichalcogenide nanotubes have been compared at different wall compositions, chiralities and diameters using the same calculation scheme. Different types of mixed nanotubes are considered - with S or Se atoms on the outer (inner) oval shell of the nanotube. It was found that nanotubes Se(out)WS(in) with average diameter (D-avr) greater than approximate to 40 angstrom have the negative strain energy. Our calculations show that the band gap is direct for zigzag MS2 and S (out)MSe(in) nanotubes (M = Mo, W) but it becomes indirect in armchair nanotubes. For the MSe2 and Se(out) MS(in) nanotubes of both chiralities, the band gap is mostly direct, except the armchair tubes with D-avr < 18 A and zigzag tubes with D-avr in interval from 18 to 26 angstrom where it is indirect.