I am building a level 8 character that has 4 levels of Rogue Unchained and 4 levels of Investigator.
The classes have a similar, but not identical, feature:
Studied Strike (Ex) – At 4th level, an investigator can choose to make a studied strike against the target of his studied combat as a free action, upon successfully hitting his studied target with a melee attack, to deal additional damage. The damage is 1d6 at 4th level, and increases by 1d6 for every 2 levels thereafter (to a maximum of 9d6 at 20th level). The damage of studied strike is precision damage and is not multiplied on a critical hit; creatures that are immune to sneak attacks are also immune to studied strike.
If the investigator’s attack used a weapon that deals nonlethal damage (like a sap, whip, or an unarmed strike), he may choose to have the additional damage from studied strike be nonlethal damage instead of lethal damage. If the investigator chose to make an attack with a lethal weapon instead deal nonlethal damage (with the usual –4 penalty), the studied strike damage may also deal nonlethal damage.
The investigator must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. An investigator cannot use studied strike against a creature with concealment.
Sneak Attack – If a rogue can catch an opponent when he is unable to defend himself effectively from her attack, she can strike a vital spot for extra damage.
The rogue’s attack deals extra damage anytime her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target. This extra damage is 1d6 at 1st level, and increases by 1d6 every 2 rogue levels thereafter. Ranged attacks can count as sneak attacks only if the target is within 30 feet. This additional damage is precision damage and is not multiplied on a critical hit.
With a weapon that deals nonlethal damage (such as a sap, unarmed strike, or whip), a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage. She cannot use a weapon that deals lethal damage to deal nonlethal damage in a sneak attack—not even with the usual –4 penalty.
The rogue must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. A rogue cannot sneak attack while striking a creature with total concealment.
Assuming all other requirements are met, do these two bonuses to damage stack with one another?
A rogue/investigator that meets both abilities' requirements can benefit from both sneak attack and studied strike
Hybrid Classes on Parent Classes says
However, unlike, for example, a hunter 5 who gains the extraordinary ability woodland stride then multiclasses so as to become also a ranger 7 and gains again the extraordinary ability woodland stride, the unchained rogue's extraordinary ability sneak attack and the investigator's extraordinary ability studied strike have different names and effects despite sharing similar (yet not identical) language.
The special abilities sneak attack and studied strike are different abilities, and their effects don't so much stack (as bonuses typically do—see here for the definition of Bonus) but merely combine for greater effect. Thus, if everything's going his way, a rogue 4/investigator 4 via this combination of special abilities can deal an extra +3d6 points of precision damage.