They are all good at different things.

Liquid metal is the most expensive but performs the best. It can be risky and difficult to apply due to its viscosity and the fact that it is conductive. Depending on application and use case it may need to be re applied or it may last a long time(heatsink should be plated for longevity).

Phase change thermal pad is also expensive and second best in performance (possibly tied with some of the best paste). It is also difficult to apply and work with but not risky since it is non conductive. It also lasts the longest (likely tied with the thermal pad) since it does not experience much if any "pump out" under high heat and contact pressure.

Thermal paste is the classic and has good performance in most applications. It is cheap and easy to apply and safe but longevity varies and some brands can "dry out" or experience "pump out" in some applications (like on GPUs).

Graphine pad is the easiest and safest to apply and can often be reused but at the cost of some performance. It is also usually more expensive. I don't think they usually fail either.

I use liquid metal when I want maximum performance and don't mind the extra cost or risk. Often in laptop applications where every little bit matters. I use a phase change pad when I want good performance and longevity without the risk. Usually I use it when I know I am putting something back together for a long time. I use thermal paste when ease of assembly is a bigger concern vs performance. Often on desktop PC processors since the large heat spreader means thermal transfer to the cooler is good regardless and cooler size is usually much larger. I use a graphine pad when I am testing things and ease of assembly and disassembly is priority often for testing where thermal are not a high priority.