Close-up filters are relatively inexpensive (though I would have my doubts about the quality of the really cheap sets) and easy to use. They come in different strengths each offering a different focussing range. All the normal camera functions are maintained.
Extension tubes don’t add a bit of cheap glass to the optical path but reduce the amount of light reaching the sensor thereby reducing the effective aperture. If you wish to retain the auto features of your lens you will need more expensive tubes.
Whichever you use you will not be able to focus at the infinity end of the scale when they are attached.
I don’t know anything about your 100-400 lens, so perhaps a user can say whether the IQ will still be acceptable with either solution.