Bike lanes on a curb are significantly more dangerous due to turning car drivers often not seeing them (due to parked cars in the way) or interpreting them as “just a sidewalk” and not properly looking for cyclists.
A lot of things need to be true for a curbside bike path to be safer than a roadside one, most importantly protection against dooring and ensuring visibility at intersections. If these measures are not taken, the result is often less safe.