Among the bacteria and archaea, which process produces results that are most similar to the results of sexual reproduction in eukaryotes and why?

This is most likely conjugation. As we know, bacteria multiplies asexually using binary fission. Basically, bacteria divide themselves and reproduce without needing a mate. Reproducing asexually is beneficial because less genetic mistakes are made, but it has its downsides too. If a group of bacteria has the same genetic composition, and there’s a disease that affects one bacterium, then all others will be wiped out as well, for they lack genetic variation.
Anyway, bacteria found a way to overcome this and reproduce asexually AND asexually. This means they can reproduce by themselves, but they can also somewhat reproduce with others through a process known as conjugation. Do not confuse this, though— conjugation is merely the exchange of DNA between two bacteria. There is no third party being produced.
A donor bacteria will insert a pilus into a recipient bacteria, and share the DNA. This creates genetic variation in a population of bacteria by jumbling up genetic material between two bacteria.
Hope this helped a little :)