I've been a machinist for 25 years. Even though digital calipers may have 4 (or even 5) digits on the display, they are considered accurate to +/- .001" just like dial calipers. I prefer a good quality dial caliper, such as Starrett, Brown & Sharpe or Mitutoyo. Verniers have less problems than dial calipers, but I find them harder to read, and when you use them constantly, you end up taking a lot more time just reading the measurements. As far as readability for old eyes, I always make sure the dial is .100" per full revolution. There are some that are .200" per rev, with a .100 mark at the top & bottom of the dial. Even when I was young and could see I didn't like that.
The divisions are so close together they're just plain hard to read. So if you need to be more accurate than +/- .001", you have to use a micrometer, and even then, it has to have the .0001" vernier on it, or else it's only good to .001". If you are checking the same bore repeatedly, pin gages are definitely more accurate, the lowest class (Class ZZ) have a +/- .0002" tolerance on the small diameters (.010" - .825").