Linux4Tegra (L4T) is NVIDIA's distribution that ships by default on devices such as the Jetson TK1. L4T is basically Ubuntu 14.04 with a custom kernel using pre-configured drivers for bootloader, kernel, OpenGL, X.Org, Multimedia, etc.
Updating Linux4Tegra repo sources
Running "sudo apt-get update" simply makes sure your repo sources are up-to-date, and thus is always safe to perform and in fact recommended that you perform it regularly (say atleast once per month).
Upgrading Linux4Tegra packages
On the other hand, "sudo apt-get upgrade" will upgrade various packages to the most recent version, and this will give you more recent software but potentially cause some package conflicts or broken software. This section lists some issues people have noticed with performing a "sudo apt-get upgrade":
Totem media player shows videos as green, no matter what format
This can be fixed by running this:
sudo apt-get remove gstreamer1.0-plugins-bad*
Web browsers for L4T
Most web browsers should work on L4T. More details are in the L4T Web Browsers page, including how to get Flash working such as for watching Youtube videos.