And I hate when people take a single case and extrapolate it as a general statement.
By that argument Ubuntu is equally unstable as they have rolled out updates that broke grub resulting in unbootable systems - not during a full distro upgrade, but as Ubuntu specific patches to LTS.
In the end, we have choice, and choice is a good thing.
Next is to login and look at the logs, especially dmesg. Find out how to open a virtual terminal, probably ctrl+alt+f1 (or f2 etc) so you can bypass the display manager to login and poke around. Or try SSH from another system. There's a couple of ideas, good luck!