just finished crunching some numbers
Poison's average defense stat over all mono- and dual-type pokemon is 64.1. Comparatively, poison's average special defense stat is 67.2
Fighting's average defense stat over all mono- and dual-type pokemon is 73.3. Similarly, fighting's average special defense stat is 72.1.
So for Poison-types, it matters slightly that you use Psyshock in order to maximize damage done in the long run, but for Fighting it's statistically insignificant/borders on favoring using Psychic. As other people have said, though, no one in their right mind is just going to let your Latios/Alakazam/Starmie/Gardevoir go to town on their Toxicroak; Psychic-types have the highest average special attack stat at 91.6 so based on the law of large numbers, it's more beneficial on average to switch in either a Dark-type mon, a bulky Steel- and/or Psychic-type mon, or a mon with exceptionally high special defense (Chansey/Blissey are the two that jump to most people's minds).
So what does game theory say you, as the original Psychic-type user should do? Well, you either have coverage for potential switch-ins and go for the mindgames, or you do them one better and let them switch in their big bad special wall and (because of empirical data on Game Freak's design theory we know that special walls tend to have relatively poor physical defense) you just use Psyshock instead. Sure, you're losing 10 BP, but because of how damage is calculated, as long as the ratio of the defending mon's defense to special defense is greater than 9/8 (the reduced form of the ratio of the BP of Psychic to the BP of Psyshock), it will always be more beneficial to use Psyshock instead.
Sorry for the math autism at the end there; I'm on break from some homework and with 30mg of Adderall freshly coursing through me I just went to town on this post. Hope it was informative and not too redundant!
