Freezing point depression is 1.86 degrees C per mole, IIRC. Even if I misremember the number wrong, the principle stands: freezing point depression is only dependent on the concentration in molality, not the nature of the substance dissolved (there may be rare exceptions). Most of Pepsi’s solutes are moderately large molecules, compared to common salts [mol wt of NaCl: 58.5; mol wt of Nutrasweet: 294] so many many grams of dissolves compounds doesn’t equal very many moles, and less freezing point depression than one might think. Carbon dioxide is a small molecule (mol wt: 44), but though it is considered “highly soluble in water” (300 vols/vol of water at STP, IIRC), 300 vols of a gas doesn’t weigh much (few grams, hence, few moles) per mole of liquid water.
Tonic water, on the other hand, is less strongly flavored and sweetened, and may have fewer moles per liter of solute.
Under identical conditions, one might expect the tonic water to freeze sooner.
But there is one other factor: the Pepsi is (by my experience) more heavily carbonated. If I read th phase diagram correctly, the effect of pressure on the freezing point is rather small – a few degrees in the pressure regime of a soda bottle.
I would guess that:
a) since Pepsi Max uses complex organic (larger molecules) flavorants and colorants and Nutrasweet is significantly sweeter per mole than sugar, the total of solutes is maybe a few hundred millimoles, for possibly under 1 degree C of freezing point depression.
b) the pressure in the bottle might raise the freezing point of water more than the dissolved materials lower it, for a net increase in freezing point
c) Pepsi is a mixture. As it freezes, crystals of near-pure ice form first, excluding the gas and solute-laden “pepsi syrup” which have a much lower freezing point. Similarly, the syrupy component will thaw first, absorbing a great deal of heat, while the near-pure ice remains solid. It takes much more energy to convert ice to liquid than to simply change the temperature. For example: it takes only 4.1 kJ/mole to warm a kg of water by one degree C, but the latent heat of melting for water ice is 330 kj/kg – so it takes over 75 times more energy to melt ice than to raise it one degree above the melting point
The Pepsi may have felt “frozen solid”, because the water ice was tightly packed (it expands as it freezes), and the bottle was taut with gas pressure, but the syrup may have been only partly frozen or melting, and acted as a significant thermal reservoir.
Which leads to my final hypothesis:
d) both the tonic and Pepsi froze, since their freezing points would be within a degree or two, but the Pepsi was more heavily carbonated (consistent with my experience), so as they froze, and the ice excluded most of the dissolved CO2. more pressure was created in the Pepsi airspace than the Schweppes, especially after the freezing ice expanded and almost completely filled the former airspace.
Moreover Pepsi is commonly sold in 2L bottles, while Schweppes (locally at least) tends to be sold in 1L or smaller bottles. This would mean twice as much excluded CO2 gas in the Pepsi, even if they were equally carbonated (and I doubt they are) yet the airspace in the Pepsi bottle isn’t proportionately larger (especially after the freezing ice expands into that space), resulting in a much higher pressure in the Pepsi. Since water is almost completely incompressible, only the tiny remaining airspace determines the final pressure, not the overall size of the bottle.
This higher post-freezing pressure caused a more significant elevation in the melting point. Note that this is an asymmetric effect: carbonated beverages would melt at a significantly higher temperature (due to the high pressure) than they freeze at.
When you discovered the bottles, the tonic had melted, but the soda had not. The Pepsi would have a higher post-freezing pressure (higher melting point); a 2L bottle would have a higher thermal mass and smaller surface/volume ration than a 1L; and the "syrupy component of the Pepsi acts as a surprisingly significant thermal reservoir as it melt. If the overnight temperature was (e.g.) -2C , it would take longer for the Pepsi to reach the melting point of its pressurized water-ice.
You presumed that only the Pepsi had frozen. The thawing of the tonic water left no evidence.