You should not be able to boot an installed system from the live usb. It is not designed for that.
If it is installing in MBR (AKA legacy) mode that tells me you selected the wrong type boot for the install USB. The live usb is hybrid and able to boot either legacy or uefi. Selecting the uefi mode to boot the install live usb will automatically install it in uefi mode. Booting in legacy mode will install it in legacy mode.
The Dell XPS laptop is finicky and it took some doing for the Live USB to be recognized as a UEFI device for the boot menu (in the BIOS configuration).
When it booted the Live USB drive in using UEFI, it then assumed that was the method to use when installing to the other external drive.
IMHO there should be the option to explicitly specify the boot style when you do the installation from the live USB (so you can boot the USB device in legacy BIOS but install with UEFI)
The option is explicit with every system I have used recently.
When booting with the live usb device plugged in and opening the boot menu I see the same usb device twice. One is just the device. The other is the device with UEFI overlaid on it. Selecting the device with uefi overlaid boots to uefi mode. The other boots to legacy mode.
That is a very explicit selection of boot mode IMHO.
How would you expect it possible to have the hardware behave as it were in uefi mode for the install when booted to legacy mode? The bios behaves differently and handles the hardware differently in each mode. In fact, if the bios is set to uefi mode only then it is not possible to boot anything in legacy mode.
The mode it uses to boot determines how the installer performs the install, not the bios. If the installer boots legacy it installs legacy. If it boots uefi it installs uefi.
Of couse! Most can boot either way when set to csm or compatibility mode. AFAIK none can select legacy boot if set to UEFI only mode, which is what I said above.
The ability to select legacy or uefi when booting from the USB is indicative that you are set to csm mode in bios.
As I said above: The mode it uses to boot determines how the installer performs the install, not the bios. If the installer boots legacy it installs legacy. If it boots uefi it installs uefi.
This may not necessarily be true for the netinst image. As I have never used that I have no first hand knowledge.
I can say that if you have 2 different OSes on the same disk and one boot uefi and the other legacy you WILL see problems in booting.