Definitely not the same angular velocity. Consider a car with two wheels that travels one mile per hour. One of its tires has a one mile circumference. The other has a one foot circumference. The large wheel rotates at one turn per hour (2pi/hr) and the small wheel rotates 5280 times per hour.
However, consider a point on the surface of each wheel. Relative to the car, a point on the surface of the big wheel moves through 1 mile of circumference in an hour. A point on the small wheel rotates moves through 5280 turns * 1 foot per turn = 5280 feet = 1 mile in an hour. So relative to the car, they both have a linear speeds (at the outer edges of the tires) of one mile per hour.