There is one important way how the small and big instruments differ, with regard to this issue: on cello and double bass, there are two very different fingering techniques used, namely, the positions above 5th are normally played as thumb position. Thumb position gives a very stable basis to notes almost arbitrarily high on the fretboard, which is why some cellists can play virtually anything that would normally be played on violin.
The downside of thumb position is that the hand is not as flexible as in neck positions, which makes smooth vibrato a bit tricky. Also you can't use the thumb as a force-balance on the other side of the neck, which I suppose makes playing bass even more physically demanding than usually. Therefore, I'd reckon, thumb position is rather more commonly and more extremely used on cello than on double bass. Add to this that bass sounds a bit weird-raspy in high registers, whereas cello can be exceptionally sweet and expressive here, and of course that the fourths-tuning is intrinsically narrower1, then I'd sum up that, yes2, cello has a substantially vaster characteristic range than double bass.
Now, with violin and viola, you don't switch to something like thumb position – ar least I've never seen it. The higher notes have to be reached while the thumb is still more or less on the neck. That seems to work pretty well on violin (though it must be really difficult to hit the notes!), but probably not so easy on viola, which – so I've heard – is a pretty arm-twisting instrument to begin with. So again, you can probably say that violin has a wider range than viola.
If I were to specify the ranges of the instruments (as in: what I'd consider reasonable to use in any score, not just as a special effect), I'd probably go with
- Violin: G3 - E7
- Viola: C3 - D5
! Ok ok, joking, violists... I know, some of you can play fourth or even fifth position!
- Cello: C2 - C6
- Bass: E1 - C4
1OTOH, 5-string basses (or low-C extensions of 4-string basses) are quite common, that of course immediately extents the range by a fourth (however, it makes particularly thumb position more tricky to bow, because you have less angle between the strings). There are also 5-string violins, violas and cellos, but these are somewhat exotic – more used by e.g. bluegrass fiddlers (or, amplified, in rock music) than by classical players.
2Since I play cello myself (and electric bass, but not double bass), I might be a bit biased here.