How to bind ⌘← and ⌘→ to previous and next tab in Safari 10?
You can use Keyboard Maestro to overwrite that ambiguous behavior in Safari and map ⌘←/⌘→ to switch between tabs regardless of any context (text field, history availability), to make it work just like it does in Chrome.
It's a pretty straightforward macro like "When ⌘← hotkey is pressed, execute “Previous Safari Tab” action" in a macro folder limited to Safari. However, Keyboard Maestro is not free.

Maybe you could also create a free Applescript service to run Window⟶Show Next Tab command (since this command ignores context, unlike the respective keyboard shortcut) and change system shortcut ⌘←/⌘→ to run that service instead (would like need to add Safari to Accessibility to allow a script manipulating menu items).