[JKT]

OmniWeb obeys the Keyboard & Mouse>Keyboard shortcuts settings in System Preferences so you can re-map the keys to something else there (for OmniWeb only). Note, the shortcuts for next and previous tab are listed under the Window menu, so you will be able to see if the changes you make take effect by viewing that menu.

Fwiw, the home and end buttons on your keyboard will do what you want if you decide you don't want to re-map the keys.

Edit: I should have said, you can re-map the shortcuts so that you need to use different combos to move between tabs, but I don't think there is any way to then re-assign command-up/down to home and end.