but I know texture-switching on an FBO is faster than FBO switching,
Where do you know this from? I remember one presentation from 2005(!)which introduced the back-then-brand-new-feature. Indeed it told, switching FBO were slower than re-attaching textures. I consider this information outdated and wrong.
FBO’s were introduced for a specific purpose, to be able to validate the completeness of it (i.e. the complex state it captures) quickly. If you don’t change a ‘complete’ FBO, its completeness can be evaluated very fast. Switching between ‘complete’ FBOs should be very quick this way, since almost no validation needs to be done.
Changing attachments of FBOs causes a new validation of the completeness which can be (according to the EXT_fbo specs) heavy.
So, how should switching between FBOs be slower than reattaching textures to them?