Same MySQL or different?

Apparently many things can share the same MySQL DB, as long as the configs for each app are named differently. So I’m wondering, is there a benefit to either running dedicated DB’s or to sharing them? I would guess that as the DB records grow, it might slow down the processing. Is this true? If so is it a negligable difference, or more noticeable the larger the combined DB records become? Why should I want or not want to share the same SQL DB between different installs?