It's not even an implementation detail. Both use, ultimately, JSR and RET instructions.
It really comes down to fetishism, which is why I don't use either of them. I am not a Fetish-Oriented Programming enthusiast.
It is also why I am not all in on Rust. Memory safety is pretty important, but it is far from the only important thing in programming. The amount of attention Rust insists I devote to it is attention I don't have available for the other things that, frankly, deserve it more.
Considering that in the last 10 years I have spent strictly less time debugging memory usage errors than preparing compiler bug reports against Gcc, putting memory correctness guarantees front and center ahead of all else seems to me a mis-allocation of my extremely scarce attention.
Attention is by far the scarcest resource available to any programmer. Allocating and applying attention where it is most needed is the central problem of programming. A language that overrules your judgment as to where your attention must be thus interferes with the core business of programming.
C++ does demand just a little more attention to memory management than some other languages, but less all the time. It pays that back by eliminating most taxes on performance, a swap I agree to.