Question about Nikon DX & FX sensor size's effects on shutter speed for a given focal length..?

Ok, I know that the DX has a 1.5 focal length multiplier as opposed to the FX's full size. As I understand it, that means that if I use a 50mm lens on the DX, I'll be getting a 75mm equivalent as compared to the full-frame sensor size standard. So, my question would be, if I used a 50mm lens on the DX and a 75mm lens on the FX (both the same Fstop).. would I get different shutter speeds if framing the exact same scene? I guess ultimately, is the only benefit of moving from a DX's sensor size to an FX's that I will get more accurate focal length frame from my lenses... or are there also quality/speed benefits?