From my point of view, the material number 2 is better. The high latent heat capacity will allow you to store more energy. But if you need to store a large amount of energy, then the distance from the heat exchange surface will play a key role. During time t, the PCM layer will heat up (or freeze) at a characteristic distance of d^2~a t, where a=lam/(ro Cp). Here a is the thermal diffusivity, lam is the thermal conductivity, ro is the density, and Cp is the heat capacity. The heat transfer to the material will be greatly slowed down during time. Therefore, it is better to have a PCM with high latent heat capacity and high thermal diffusivity.

In my opinion, the ideal properties of a PCM would be:

-High thermal conductivity

-High latent heat of fusion

-Low specific heat capacity in solid state

-High specific heat capacity in liquid state

-High density for both phases (for compactness)

So, of the above alternatives, number 2 would be my choice.

High latent heat directly correlates to system size/weight volume. There is some academic discussion on whether specific or volumetric latent heat is more important for certain applications, but in either case higher is always better, as the system size will scale directly with energy storage requirement according to latent heat.

The need for high/low thermal conductivity is directly related to the required system heat rate. In very slowly changing systems, a low thermal conductivity might be tolerable. Whether or not the diurnal cycle, or the fraction of that relevant to charging/discharging time, and environmental heat loads are sufficiently 'slow' for typical PCM properties (kth ~ 1 W/mK or less), is of some debate. If you look at the literature, quite a bit of effort has been spent trying to overcome the low thermal conductivity challenge through heat spreading structures, high conductivity additives, etc., as low kth directly impedes thermal charging/discharging. These structures/additives generally detract from latent storage density, as the structures/materials take up volume that would otherwise contain latent storage material.

Most traditional PCMs have very low thermal conductivity with an impact on system response. Those materials with higher kth are generally less applicable to building scale TES. Low temp metallics are an area gaining interest for small, high power density applications, but density and expense make them hard to scale. Salts can be better, too, but usually only at higher temperatures, with hydrated salts (back to generally low kth) fitting into the environmental control temperature range.

Regarding formal studies of 'what's better' -

There are only a few studies that have developed 'performance metrics' or 'figures of merit' for PCMs. The four that come readily to mind are

2000 - TJ Lu - Article Thermal management of high power electronic with phase change cooling

2016 - Shou, et al. -

Article Figure-of-merit for phase-change materials used in thermal management

2016 - PJ Shamberger -

Article Cooling Capacity Figure of Merit for Phase Change Materials

2018 - PJ Shamberger & TS Fisher

Article Cooling power and characteristic times of composite heatsink...

Worth noting, all of them have FOMs derived from a 1D heat transfer model focused on keeping a heat source cool with the PCM directly between source and sink. They also focus the higher power problem. As such, the PCM is a thermal bottleneck, and that comes out in the Figure of Merit.

They all produce a Figure of Merit of the form:

FOM ~ thermal_conductivity * density * latent_heat

(with some variation depending on exact model form)

Note (1) the density*latent_heat product (e.g., volumetric latent heat) is important, not just latent heat itself. This makes sense as volume directly relates to thermal-path-length. More latent heat close to the source is better than lighter latent heat for their models. (2) thermal conductivity is on equal footing with latent heat. The latent heat does you no good if you can't get the heat into it, and once melting begins the phase front moves away from the heat source, amplifying the penalty from low kth.

Now, what of this is applicable to building TES? A good question, and probably changes a lot depending on whether you're talking about HVAC or building material design, and how weight/space constrained you are. I believe Luisa Cabeza's group has done a lot of good TES work focused on building and environmental control. Recommend you look into her group's publication list for some good info. (see https://www.researchgate.net/profile/Luisa-F-Cabeza/research)

Based on the application, generally, High thermal conductivity

-High latent heat of fusion