On the website torah.org an overview is given of ritual objects that, in case of their disposal, require a strict genizah (buried in a cemetery and sealed in earthenware or hard plastic, preferably with or near a Torah scholar) or standard genizah (buried any place that will be undisturbed).
For the bayith shel rosh (even without parashiyos) the strict genizah is considered necessary, whereas for the bayith shel yad (without parashiyos) a standard burial is deemed sufficient.
The source referenced on the website is Ginzei ha-Kodesh 6:6. I can't seem to find the source and my question is: why is the bayith shel rosh itself (the case of the head-tefillin, even without a scroll inside) considered more holy for the purposes of genizah than the bayith shel yad (the case of the arm-tefillin)?