If you have a built in seating area that is taller than the standard counter height you will might be better with a bar stool.
Standard counter height breakfast bar.
Counter height bars stools are used with 35 to 37 inch high counter tops.
Counter height i think is the best compromise b w the two.
Construction conventions standard conventions support the 42 inch bar height.
A breakfast bar is either a full kitchen island or a countertop overhang with a height that has enough room for the legs and a size that can accommodate ample room for meals.
A counter chair might have a seat back and arm rests but most.
Counter height bar stools usually measure 23 to 28 inches from the floor to the seat.
However it can vary.
Most kitchen countertops are around this height to match the height of standard kitchen appliances.
Counter chairs measure between 24 and 26 and at that height often do not fit well under a standard height dining room table.
In kitchens some bars are 36 inches the height of a regular kitchen counter while others feature a raised element that brings part of the counter up to 42 inches.
Wet bars are always built at the standard bar counter height of 42 inches.
A typical breakfast bar counter has a standard height of 42 inches 107 centimeters and a depth countertop overhang of 12 to 16 inches 30 to 40 centimeters.
For young children and older people table height is the easiest and safest height bar height otoh is often difficult for both age groups to get in to out of.