I'm not so sure about ps4 as I'm waiting for Destiny to buy one, but if it's like ps3, the digital copy will likely run and load relatively faster.
A physical copy will install only the minimum files required, relying on both the blu-ray disk and the ps4's HDD to run. A digital copy, on the other hand, will have to solely rely on the HDD; in that case there would be no need for a blu-ray disc to spin and no latencies related to accessing and reading operations.