Microsoft has given some small insight as to why games take longer to install compared to the PS4 system.
As a owner of both consoles, I do notice that games install much faster on the PS4 than they do on the Xbox One. There are some exceptions, but the general consensus is that the PS4 is faster in that department. The only games I know that are slow on both consoles were NBA 2K14 and 2K15. Both games required around 50GB which is why they took so long.
Xbox Head Phil Spencer talked more about the installation times for the Xbox One during a podcast with IGN. One of the reasons why early games like Ryse: Son of Rome and Forza Motorsport 5 took some time to install was because the Xbox One was designed to be always-online. Spencer said once they removed the always-online aspect, “flow of the installation code is not as flawless as it could be“. He even had a team of his own people to investigate the install times of the Xbox One compared to the PS4. He said some gamers are faster to install on PS4, while others are “significantly worse.”
He says the slower install times should not be blamed on Xbox One’s Blu-ray drive or hard drive however. This is because they have similar specifications to the PS4. He actually admitted he’s not sure why Xbox One installs games slower than PS4, but agrees it’s a problem to address. He and his team want to find out what the problem is and will hopefully make installations faster in the future.