There are two main criteria which determine how we will finger a passage in (or to) Thumb Position: technical (“which fingering is the most secure?”) and stylistic (“which is the most appropriate?”)
The difference in style (aesthetics) between the Romantic Period’s tendency to swoop and soar, and on the other hand, the Classical Period’s discretion and “cleanliness” (see PEDAGOGICAL ORDER BY EPOCH IN THUMB POSITION), has profound fingering implications for the cellist. We can finger passages “Romantically” (staying on the same string) or “Classically” (playing “across” the strings).
In “Classical Style”, this Beethoven example could be played across the strings (as indicated in the suggested fingerings). This “stay- in-one-position” fingering also makes the passage infinitely easier because the use of swooping romantic glissandi to help secure those large shifts would be stylistically inappropriate. In spite of the shifting difficulties, most cellists however choose to play it on the A string for the more soloistic sound quality. And, what’s more, this is Beethovens Opus 56: we are now coming into the Romantic Era so perhaps the “classical” fingering is already outdated (or almost). The Tosca theme is a perfect example of a soaring Romantic melody that desperately wants (and needs) warm vocal glissandi to accompany the large melodic leaps. Fingering it “across the strings” in such a way as to eliminate these gorgeous glissandi, as though it were a charming classical-style melody would be completely out of style.