(1) Am I correct that the Banach-Tarski paradox (BT) was discovered before the Sierpinski-Mazurkiewicx paradox (SM)?
(2) In many ways SM seems "more powerful" than BT. (a) It uses two pieces instead of 5; (b) It operates in 2D while BT requires 3D; (c) it is much simpler; (d) it does not require Axiom of Choice.
BT is "more powerful" because (e) it operates on SOLID bodies; (f) the input set is uncountable and has non-zero measure, while SM operates on a countable set.
(Does this summarize the difference in constraints? What am I missing?