Should I buy a 500gb external hard drive and a 500gb hard drive for my new computer?

I want to transfer all of my files from my existing computer (photos & music) to my new computer via external hard drive but I'm unsure if I should get a large external or a large hard drive for the new computer. I was thinking about a 500gb external & 500gb on the new one.

A friend told me to get a larger external & smaller hard drive for the new one so that the computer would run faster, is this true?

500GB Mini Portable USB 2.0 External Hard Drive GB 1 wd