AVE did a good video on cheap digital calipers:
https://www.youtube.com/watch?v=KnDype-j3hkUpshot: Cheap calipers can be perfectly accurate (especially for bike use) but they never really switch off, even when the display is off, so the batteries run flat even when unused. They also don't have brownout protection\a low battery warning and when the batteries start to run down they give erroneous readings.
Solution: store them with the batteries out or buy a bunch of cheap coin cells off the internet in preparation. Keep something of known dimensions around to test if you are getting suspect readings.
His findings mesh with my observations. I have several sets of calipers, cheap and expensive, and they are all accurate enough. Everyone I know with (cheap) digital calipers finds they eat batteries.
Re: dial calipers:
I bough some nice Starrett ones a while ago but I don't like them. In use the dial isn't as easy to mentally parse as I expected and the whole-millimeter reading is not as clear as it could be. The incredibly fine rack and pinion mechanism needs only the tiniest just-visible speck of sawdust to skip.
Dial calipers lack the useful features (zeroing, units etc) and easy readability of digital ones. Vernier calipers are simpler and are easier to read once you are used to them in my opinion.