The question is weather a CPU or dGPU is "better".
If we are talking about an APU the answer has already been given. A good dedicated card is going to be faster but it will use more electrical power. An APU could be a good thing in a power restricted environment like a laptop or if you just don't need better graphics. A modern APU is plenty for non-gaming day to day use. For the foreseeable future a dGPU is going to be better in a desktop with a big power budget.
At some point it looked like the OP literally intended to compare a non-APU CPU to a GPU. These devices are not really directly comparable. A modern multi core CPU is a fast general purpose device that can do a few things at a time, like a work crew of a few smart handymen. They can do anything from flooring to roofing and they are each really fast. If they need to do something new they will figure it out and get it done. Putting up a roof might take them all day but they can do such a job. When a CPU proper (not an APU) is asked to render video it is call "software rendering".
A GPU is less flexible and would be more like a couple thousand slower dudes who only know how to shingle roofs and who don't speak English. If you need new carpet these are not the guys you call, they can't do this job at all and they never will be able to. If you need a new roof put on in seconds these guys can handle the job.
A GPU's speed comes more from massive parallelism and a more specific workload with specifically tailored hardware while a CPU's speed comes more from a higher clock.
Check out this picture (I remember this like yesterday as it cemented what a video card was in my mind):
Notice that the software render on the left has fewer colors and lower resolution. The picture shows them both at 30FPS but I can assure you that GL Quake was much much smoother on a 3dfx card than the choppy, pixelated, slide show that was the software render.
Now we have come a long way and a modern CPU would do a better job but the principle is the same. We have a lot more pixels to push (shingle) these days with 1080p or 4k monitors.