It used to be that the default fullscreen resolution of webplayers was the default standalone resolution (as defined in Edit → Project Settings → Default Screen Width/Height), regardless of the embedded webplayer size.
… but it doesn’t seem to be true anymore: now the fullscreen resolution is the closest one to the embedded size. Was this broken in 2.5.1?
A workaround is to use a GUI fullscreen button and use SetResolution() instead of just fullscreen=true… but if the user goes right-click>fullscreen, you’re screwed.
The hack:
if (GUILayout.Button("Full Screen"))
{
if (!Screen.fullScreen)
Screen.SetResolution(1024, 768, true);
else
Screen.fullScreen = false;
}