The technology in theory is similar, but the implementation isn't exactly the same.

Without knowing exactly which model, or even which manufacturer made your camera, it is difficult to be very specific. There's a large difference in performance between different models and lenses.

It always starts with light, so let's begin there. The amount of light used by each pixel of an on-sensor PDAF array is much less than the amount of light used by each pixel of a dedicated PDAF array.

• The dedicated PDAF sensor pixels are several times the size of, and thus more sensitive than, the pixels in the image sensor. The light falling on them is gathered from an even wider area through the use of the splitter and micro-lenses between the reflex mirror and the focus array.
• The pixels in most cameras with on-sensor PDAF have a Bayer filter or other form of color filter over the light wells. This means a good portion of the light that falls onto a pixel doesn't make it into the light well. Traditional PDAF sensors are monochromatic, so there is no need for any color filters.
• Getting the data from the sensor is another potential speed bump. Since the data from a dedicated PDAF sensor is gathered from lines only a single pixel wide, the data can be read more quickly than that coming off a full sensor that is also being used for metering and possibly WB computation as well.
• Most cameras with PDAF use a hybrid form that includes elements of both PDAF and CDAF. Any CDAF system requires more stages than a PDAF system as it is a "move and measure" system that repeats the process until it finds the distance that produces the most contrast. A PDAF system can measure once, determine how far and in which direction the lens is out of focus, and then move the lens. A CDAF system must take at least two measurements to determine which direction to move the lens to get more contrast, and then must sample until the lens has moved past focus and contrast begins to fall off.
• The half-silvered portion of the main mirror that all light falling on a dedicated PDAF sensor array must pass through does reduce the light by 50%, but even with this loss the dedicated sensor is still getting much more light per pixel for the same amount of light entering an equivalent lens.

Having said all of that, I highly suspect another big reason for the difference lies in the design of the lenses attached to the respective cameras. With traditional DSLRs, PDAF speed can vary quite a bit on the same body depending on the lens being used. The focus motors on lenses designed for the typical on-sensor PDAF cameras are more comparable to consumer grade DSLR lenses, and even fixed lenses on bridge cameras, than to higher end DSLR lenses. Overall design, weight of the elements being moved, the size and type of motor used to move the lens, and the firmware that controls it all have an influence on the overall speed and accuracy of the lens' mechanical focus system. If the on-sensor PDAF camera is even capable of interchangeable lenses, there may be faster lenses (aperture and focus drive) available for a premium. Remember that aperture is figured on actual, not effective, focal length. Some of the cameras in question, like the Fuji X100S, have APS-C sized sensors. When this is the case the aperture sizes are comparable to lenses used on APS-C DSLRs. But other cameras like the Nikon 1 series have 1" sensors with barely half the linear dimensions and less than 1/3 the surface area of an APS-C sensor, not to mention that they are dwarfed by the 7.5X larger 36X24mm full frame sensors. When comparing the lenses for these cameras, the absolute size of the diaphragm is smaller for a given f-number and angle of view because the focal length for that same angle of view is shorter. The mass of the optics in such lenses is less than that of more typical faster focusing DSLR lenses, but the space available for the motor that drives the movement of those optics is also much less.

Thanks to jrista for the information in his comments regarding this answer. Much of the correct information on this heavily revised answer is his. All of the mistakes are mine. B-)