Any suggestions on which one has faster onset of symptoms: intoxication or infection?

Impossible to say: Because it depends on what you are talking about - intoxication with what and infection with what? If you chug a pint of rum, you can die from alcohol poisoning if you are alcohol-naive. Literally within a half-hour or so, ditto with a heroin or Oxycontin od. Meningitis can go from a mild cold to death within hours as well; other intoxications and infections are slower and more chronic.