I think this would be more accurately framed as a chemistry question. Without knowing the underlying chemistry of extraterrestrial organisms, we can't really ma

I think this would be more accurately framed as a chemistry question. Without knowing the underlying chemistry of extraterrestrial organisms, we can't really make meaningful statements about how they might interact with DNA based life. You can certainly imagine simple, yet highly adapted, microorganisms evolving in the Martian environment where competition is scarce. In this situation, our quite robust terrestrial organisms might overwhelm native populations simply because they are much more adaptable to change and competition with foreign bodies. This still doesn't even touch on the compatibility of the biochemistry. Perhaps life from either origin attempting to consume one another causes volatile chemical reactions, destroying one or both organisms. In this scenario it would come down to which (if any) evolves the necessary chemistry to consume and/or avoid the competition first. More broadly, the introduction of any foreign chemistry at all could be destructive to native populations, let alone the introduction of new life forms. Given the complexities involved and lack of data, I wouldn't feel comfortable making a case one way or the other.