Spoiler Plasma Pistol are assumed to be typical mixed type damage weaons, and I use the term Plasma Pistol interchangeably with the term mixed-type damage weapon.
Phys = Physical
En = Energy
DT = Damage Threshold
DR = Damage Reduction
So I went through a few examples just to see how different damage and resistance types might work, and here are some thoughts on the situation:
I'm going to use the same colour coding as Robotoh above, with the addition of orange used to refer to mixed damage in general:
For my examples, I'm using a Laser Pistol, a 10mm Pistol and a Plasma Pistol, giving them all a total damage of 10, meaning respectively 10 Energy, 10 Physical, and 5 Energy + 5 Physical damage.
If we use a system relying on DT like in Fallout New Vegas:
Against different armours possessing 5DT En, 5DT Phys, and 2,5 DT En + 2,5DT Phys respectively.
Then the the single damage weapons always outperform the Plasma pistol: while the plasma pistol does a steady 5 dmg, mixed or otherwise, the other weapons can go anywhere from 5 to 10 damage.
I then assumed assymetrical DTs for armour, like 3DT Phys. + 6DT En. ; 6DT Phys + 3 DT EN ; and in-between the two 4DT Phys + 4 DT En
In this scenario, Plasma wepons are completely outperformed, dealing vastly inferior damage in every case, sporting a sub-par 2 dmg in every category, while the other weapons ranged from 4 to 7 damge.
A fix for this situation would be to multiply the total damage dealt by Plasma weapons by 1.5, which would then in every case, put them in-between the damages for either purely physical or energy type weapons, meaning a range of 7,5 to 10 in the first example, and a range from 6 to 7 damage in the second example. This would put Plasma weapons a bit above middle-ground, giving them a damage output in-between what can be achieved by either Physical or Energy weapons, while being a tiny bit better against armour with equally distributed DTs. However this would only work for DTs that would soak up around 50% of an incoming shot. With damages per shot vastly surpassing the DTs of different armour, Plasma weapons would become vastly superior to any other weapon out there, simply because the DT wouldn't be able to block enough of the damage, and Plasma/mixed damage weapons woud then have up to 1.5 times more damage than any other pure damage weapon. On the other hand, Plasma weapons would become ridiculously weak against armour with high DTs in both categories, as for example Power Armour. This would, without further tweaks, make mixed damage type weapons the best single shot weapons by far, while making them pretty bad for rapid fire weapons. Either way, the balancing of different types of damage and mixed damage is quite difficult with a DT based system.
If however we assume a system based DR like Fallout 3:
Assuming a DR of 60% for either only Energy, only Physical, and both damage types, then again Plasma does more damage than a poorly chosen weapon, and exactly the same amount of damage than either against armour possessing equal DR for both types of damage.
With assymetrical DR, meaning 60% Physical and 80% Energy or the other way around, then Plasma lies again in the middle ground, dealing always more than a poorly chosen weapon, but less than the optimal one.
All in all, a system based on DR would allow to place mixed damage weapons in between Laser- and Physical-based weapons, allowing for an easier balance of power levels.
And with a system using both DT and DR... well I haven't come to that just yet, since I'd need to compare DPS and Damage per shot etc.
Obviously, balancing with a combined system plus different damage sources will be quite tricky, having to deal with mixed damage types going from sub-par to grossly over-powered, and the balancing of DR.
tl;dr: Mixed type weapons COULD work with a DT based system, but would require quite a bit of balancing for the weapons not to be either underwhelming or too powerful.
The system is most easily applied to a DR-based damage system, with all the disadvantages such a system entails (meaning DPS becoming the determing factor for weapon power).
In consequence, we might see a return to a DR-based damage system in Fallout 4, since it would be easier to integrate different damages and damage resistances.
I will not discuss which system would be better game-play-wise, or if a hybrid system would be best, since the pros and cons of DR vs DT are being discussed thoroughly in other threads.
All this of course does not account for possible perks and how they will modify damage, so keep that in mind.
I'm just excited they decided to mix it up some and allow what might even become tactical combat and preparation.
Edited for typos