As long as I know the both can be used interchangeably.

The main difference is the meaning they could take which is very subtle and difficult to explain.

Case where “bêtise” is used

*A childlike misconduct

• A childlike misconduct eg: Throwing tomato sauce on the floor
• A non-crucial error oftenly eg: Use the wrong word in a sentence

“bêtise” is also a candy but… well nobody cares

Case where “sottise” is used

• A stupid sentence eg: What is the color of the white horse?

After reflexion I would say that sottise is harder than bêtise which is more smooth.

“Tu dis des sottises” > “Tu dis des bêtises”

The main difference is the adjective used to constitute the noun meaning that :

• Bête => Bêtise
• Sot => Sottise

You also have the following synonyms :

• Idiot => Idiotie
• Con => Connerie
• Stupide => Stupidité (but this one rather refers to the concept of being idiot than the act itself)

So if you want differences betwwen “bêtise” and “sottise” (and “idiotie” & “connerie” too), you will have to look for nuances between the adjectives behind the names.

La principale différence se situe au niveau des adjectifs utilisés pour former le nom :

• Bête => Bêtise
• Sot => Sottise

On peut également citer les synonymes suivants :

• Idiot => Idiotie
• Con => Connerie
• Stupide => Stupidité (mais ce mot désigne plus le concept d’être idiot que l’acte en lui-même)

Pour trouver les différences de sens entre “bêtise” et “sottise” (mais aussi “idiotie” et “connerie“), il faut donc regarder du côté des nuances de sens entre les adjectifs derrière les noms.

Hugo uses the two terms bête and sot with an implied contrast in Les Misérables (P3B4Ch4):

La vanité a un envers et un endroit; l’endroit est bête, c’est le nègre avec ses verroteries; l’envers est sot, c’est le philosophe avec ses guenilles. Je pleure sur l’un et je ris de l’autre.

For context, the speaker, Grantaire, has just claimed that vanity is that with which nothingness (Zéro) dresses itself up in order to not walk about naked (a possible Emperor’s New Clothes reference); and in that context, envers and endroit refer to the inside and outside of the clothing (not to a wrong and right side of vanity per se.)

I believe Hugo means bête and sot to be read as contrasting terms, particularly in light of the subsequent sentence, in which Grantaire says he weeps for the one and laughs at the other. I would read bête here as “primitive” or “atavistic” as against the perverse stupidity of the philosopher, all of whose learning and thought has only led him to flaunt his rags.

That said, this difference is clearly very specific to this usage and context.