I am not a fan of small temporary spare tires even though they store easily. When touring I need to have a full-sized spare that allows me to complete the tour without delay. There are remote places where modern tires sizes are not available and in our case we had ferry crossing reservations made six months earlier that could not be changed. We were on a schedule and only complete replacement of a blown tire with another of the same size and capability would work.
I came to this realization when our last car had run flat tires that have a limited range after puncture. After a tread separation problem that made a full sized spare the only roadside alternative to a tow truck and huge delay, I was sold on carrying the bigger spare.
Perhaps a small donut spare for city use is OK but when travelling across the country and into remote areas a full sized spare mitigates the risk best, in my opinion.
Tool and jack storage inside the full sized rim is not a problem and only a few pieces of packing foam are necessary to reduce rattles.
In the real world you can justify both sizes of spare tire but for long distance touring take the full sized one.