I recall in 1.0 and earlier the arrest success chance was a flat 50%. Literal coinflip, like many things Rimworld. Psychology's stat is based on pawn personality so I'd probably go with that one over vanilla.

Here's a clearer picture of the differences in the current version, at least as far as I could find. Feel free to remove this if you'd rather not have this information posted.

Psychology
ArrestPeacefullyChance * opinionFactor (0 to 1, linear with opinion from -100 to 100 of arrester by arrested) * sameFactionFactor (50% higher for same faction, normal otherwise) * mentalStateFactor (1/5 chance if arrestee is having a mental break)

ArrestPeacefullyChance is base 0.02, increases by social 5% per level, affected by talking (90% weight)

This is not a bad approach, in my opinion. I think the base chance is a bit low, but it's a good list of factors combined in a reasonable way.

Vanilla (1.3)
ArrestSuccessChance is base 0.6, plus 7.5% per level of social, affected by manipulation (90% weight, 5% allowance before effect, 100% max).

I'm not aware of whether or not this figure is modified in the game's computations, as above with the factors. I suspect it is a simple check against a uniform variate, with opinion, faction, and mental state all ignored.

From the differences, I gather Psychology conceives of arrest as involving talking the person into coming quietly, while vanilla's implementation is partly about talking to them and partly physically subduing them. Not that my opinion really matters here, but I like Psychology's approach better. Would you consider suppressing the vanilla stat from showing up in-game? Or perhaps adapting the vanilla one to use Psychology's formula?