@Simon: The stock kernel for Ubuntu is 4.4.x for now. `uname -a` will show which one you have.
I definitely had very poor experiences with kernel 4.4.x on both TB16 and WD15. I chose 4.9 because it is a designated LTS version from the kernel developers (not the Ubuntu developers, mind).
I upgraded the kernel myself. It is pretty easy if you are comfortable using the console, sudo and apt-get. Just google "ubuntu upgrade mainline kernel" for instructions.
Regarding installing drivers on Windows, I have no idea which chipset drivers actually end up patching the firmware vs which are just used within Windows. So I simply installed everything I could find inside the categories "Chipset" and "Dock". There are some detailed instructions on what order to install them here, but I just installed them randomly myself.
@tfnico hmm... it looks like in February Ubuntu brought out Ubuntu 16.04.02 with kernel 4.8. Were you aware of this and what made you go for kernel 4.9 never the less?
I checked my kernel and it's version 4.4 even though I order the laptop well after February. I have asked Dell support about this but no response so far.
Found this link  showing how to upgrade Ubuntu 16.04 to 16.04.02 and it looks like by default it does not include upgrading the kernel but there is an option to include the kernel.
Waiting to hear from Dell before I decide what to do...
@Simon: I got rather desperate back when I was still on the WD15 for fixing the display crashes. So I tried every almost every kernel version as soon as they came out hoping they would fix the issue. Things were already a bit better on 4.6 I think.
I got my laptop in November (right after the 9360 landed in Europe), and besides from the kernel I've followed the regular stock system updates, hence I am now also on Ubuntu 16.04.2 LTS, with the self-upgraded mainline kernel.
@tfnico: Thanks for the quick response.
So Dell support walked me through upgrading the kernel from 4.4 to 4.8 and after that the external monitor and suspend / resume problem is fixed! :-)
Mysteriously on subsequent reboots with kernel 4.8 the bluetooth did not work any more :-( dmesg said "Bluetooth: hci0: Failed to load Intel firmware file (-2)". I fixed it by following the instructions here  to re-install the bluetooth firmware.
Mysteriously on subsequent reboots the bluetooth did not work any more :-( dmesg said "Bluetooth: hci0: Failed to load Intel firmware file (-2)". I fixed it by following the instructions here  to re-install the bluetooth firmware.
I've been using the TB-16 for several days and it seems stable. So far I would actually recommend buying it if your use case is the same as mine. Here are a few notes about my setup if it helps anyone else.
I noticed on the parallel TB15 support forum that someone has had success with most issues (bar booting) with the latest 4.12.4 kernel. Has anyone tried this with the TB16? If so, do you aware if there are any issues running the 4.12.4 kernel under Ubuntu 16.04?
I recently purchased a TB16 dock and I'm running with following configuration:
Before connecting the dock, I updated to the latest BIOS (1.4.18 for the 9350) and also updated the thunderbolt firmware and associated windows drivers according to the instructions provided by tfnico (using a bootable Win10 USB drive).
Much to my relief, everything just worked after connecting. The Gbps ethernet issue was fixed in a recent kernel update (some time around 4.12.4 I believe) and it's been rock stable for the past 3 days with no connection errors. As such, it's no longer necessary to limit the connection speed to 10/100 with the latest kernel (it's possible the patch will be backported to the current Ubuntu kernel). Haven't experienced hangs when I boot with the dock connected, nor when I hotplug or unplug after boot. Also haven't yet run into any suspend/resume issues either in various combinations of plugging and unplugging the dock before/after suspend.
The next 4.13 kernel will apparently include several updates to the thunderbolt infrastructure, including control of security levels and firmware updates. I'm hopeful this will finally allow for native firmware updates without the need for a Win10 USB. All in all it looks like the TB16 is in good shape when running with the latest firmware updates & linux kernel.
Just to add, the backport fixing the TB16 ethernet issue is currently in the xenial-proposed repository:
It's awaiting verification so perhaps it's worth installing the latest 4.10 hwe kernel from the 'proposed' repository.