The former: once you have COVID you're immune to it. Unless a strain totally evades the antibody response of recovered individuals (very unlikely), then they're no longer capable of spreading it.

So if there's overall less replicants of one strain then the other, then the population will effectively select for the more infectious one. Actual geography of course is also key here though: if a carrier flies over to an unexposed area with any strain, it's going to take over if the other one doesn't make it there.