https://w3c.github.io/uievents/#event-type-keydown says that
If the key is the Enter or Space key and the current focus is on a state-changing element, the default action MUST be to dispatch a click event, and a DOMActivate event if that event type is supported by the user agent.
This happens in all browsers.1,2
The problem is that Firefox does not set the ctrlKey and shiftKey attributes on the dispatched click event. Webkit and Chrome1 do. I think it makes sense for them to get set, though the spec should probably make that explicit.
Also all the other modifier key attributes that apply to both keydown and click events. (might be worth checking whatever Webkit/Chrome do for a list.)
1 Chrome does not dispatch the click event if Ctrl is being held down.
2 I did not check for the DOMActivate event, as I am only interested in the click event.