It does have a consistent shortcut: Command+{ and Command+}. Works in every app that has tabs.
(Now I know why the terminal has those weird command+Ö and command+Ä shortcuts, Ö and Ä are presumably where { and } are when you use the US keyboard layout. Those pesky umlauts. By the way, { and } are alt+8 and alt+9 – also where the normal brackets are when using shift – on a German keyboard. Oh, and command+Ö or command+Ä totally don’t work in Safari. You have to use ctrl+tab.)
I guess pick the shortcuts that cover the largest subset of apps you care about.