In Safari, if you are not currently editing a text field, cmd-shift-left and cmd-shift-right can be used to switch tabs. This appears to be unsupported in Orion (Version 0.99.113-beta (WebKit 613.1.12)).
(Somehow I never knew until today about the alternatives of cmd-[/cmd-] and ctrl-shift-tab/ctrl-tab, both of which work in Orion, Safari, Chrome, and even Terminal and iTerm. And unlike cmd-shift-left/cmd-shift-right, they don't stop working while editing text. But I'd like to keep using the shortcuts I'm familiar with…)