If I had 8gb of RAM and a dedicated graphics card with 8gb of VRAM of the same memory speed V.S. 16gb of RAM with an integrated GPU (asuming they are all of the same memory speed), why would the integrated gpu set up be slower? or would it be?
Depends on the gpu. Also most dedicated GPUs don't use standard ram like an igpu has to, they normally use faster ram as they are not limited to sharing system ram.
PNow a dedicated gpu with 8Gb of vram is going to be a higher end card and will decimate any igpu. However it will also cost alot more, use more power and produce more heat.