[...] Both should be able to inflict sneak attack [...]
AND, you shouldn't be able to use an off-hand attack if you didn't also used an attack action at the same turn. Otherwise it means that characters with off-hand get to attack with a bonus action.
a) The actual rules do not allow two sneak attack per turn, for obvious reasons of game balance. Will not argue for nothing on that point. It is a hardcore official rule, which DMs pretty much never change.
b) Official rule reading (by many for years) is that YOU CAN attack only with your Bonus Action offhand (but do not add Ability modifier unless you have a special feature exception). This logic does not apply to Monk's extra unarmed attack for which you must first do a normal Action attack (Monks are not in the game, but just saying for your D&D knowledge).
EDIT : I was wrong or rather the popular discussions about this on the web were wrong. You must first do the attack Action, before using your offhand.
