Thanks to etherfish for pointers. I have done some more research:
Turns out that this has been broken by an RFE, which introduced first version of another patch, which enabled S-down/up to scroll one line, thus broke the tabbing.
Later this has been addressed few times (e.g. by editing the patch and trying to change that to C-up/down), but that was not really accepted so currently the situation is not solved, save for adding C-T, presumably as a hotfix (... better than no shortcut at all).
I have posted this as bug against Fedora
So what can we do now?
Wait for Fedora maintainers to fix the problem (or propose
Build urxvt yourself from upstream.
Use different version of tabbed, like tabbedex.
Use local copy of
tabbed, adding a third shortcut that works on
both distros (either add that to ~/.urxvt or edit the system-wide file).
Update: Awesome, about a day later, patch to the bug is already submitted and on its way to release. Patches that broke this on Fedora are being removed so that S-Down will soon work again. Thanks, Fedora devs!