For best ergonomics, both should be well supported.

If I'm programming and want to look up something in the docs, then it's annoying to switch to the mouse and then back, but I pretty much have to with traditional browser UI. (Or tab through a million links to find the right button to click, use cursor keys to scroll, etc.)

Similarly, if I'm just scrolling around with the mouse, then I should be able to do everything that I can with the keyboard (apart from text input). The context menu is good for discoverability, but being context-dependent makes it impossible to rely on muscle memory.