AFAICT the programming port is much more easier to use for uploading a new software, although much slower too.
Unless you really need a super fast serial link for Serial writes (up to 849 Kbps with native USB), the programming port is the good choice.
I guess some DUE users could explain the issue better than me, but the USB OTG HS is clocked at 480 MHz, hence as soon as there is the least electrical issue with the USB cable/sockets, UOTGHS will try to find another COM port.
A "deep" diagnostic of the native USB issues would certainly require an extensive knowledge of USB 2.0 OTG HS protocol and/or writting a new version of SerialUSB.