Micrometer calipers measure thickness. Vernier calipers can measure both thickness and inside diameter. For the same least count and accuracy, both are similarly priced. Do micrometers have any advantage over verniers (besides size- micrometers being compact)?
Micrometers tend to be used for higher precision measurements and are usually specific to one particular type of measurement (thickness, depth, bore etc) they are defined by their vernier screw mechanism which can be adapted to various functions (the fine feeds on lathes use a similar principal).
Vernier calipers (and their dial and digital equivalents) are a bit more convenient to use and are more versatile, having a larger range of measurement and being able to measure, thickness, length, diameter, bore and depth in the same instrument.
It's common to use vernier calipers for general measurements where reasonable precision is required (say to around 0.1 mm) as they can be fairly inexpensive and are plenty accurate enough for a lot of tasks eg checking if a drill is 10 or 10.5 mm
Micrometers and the like tend to be reserved for higher precision tasks like fine machining and grinding where accuracy better than 0.1 mm is required, especially for repetitive measurements over a narrow range.
Obviously precision will vary with quality but typically a micrometer will have better precision than a vernier caliper in the same sort of price range.