In theory, they should be pretty close. But in practice USB 3.0 has been shown to be a good bit slower than SATA III. Not really sure why...maybe there is just extra overhead with USB 3.0? Though I have heard that many USB 3.0 ports don't actually run at full speed.
You actually have it backwards. The HDD in the Xbox One and the PS4 push data at the same rate 3 Gbit/s (300 MB/s) transfer speed. And the USB 3.0 on the Xbox One is faster than both at 5 Gbit/s (625 MB/s). Games on an extral HDD load fast as more data can be transfer over the same period of time. Someone put a SSD external drive on an Xbox One and it ran even faster.
Also, if Sony had external USB 3.0 drives to the PS4 there is no reason not to assume an fast external drive would also run games quicker than the orignal HDD. (I am assuming a PS4 has USB 3.0.)
Notes: USB 3.0 faster than internal: http://www.dualshockers.com/2014/05/26/xbox-ones-external-storage-can-improve-loading-times-with-games/
Someone tried a SSD in a PS4 with a little improvement: http://ps4daily.com/2013/11/ps4-ssd-upgrade/