Modern combined cycle gas turbines offer thermal-to-electric efficiency over 60% (on a lower heating value fuel basis) at full design load, e.g. this General Electric system at 64%:

https://www.ge.com/news/press-releases/ha-technology-now-ava...

Approximating natural gas as 100% methane, that means the thermal-to-electric efficiency on a higher heating value basis is more like 57-58%:

https://en.wikipedia.org/wiki/Heat_of_combustion#Heat_of_com...

But neither of these efficiency measures account for district heating with waste heat.

60% would be terrible thermodynamic efficiency for a cogeneration plant. Modern CCGT systems crack 60% thermodynamic efficiency for just the electricity generation. With cogeneration, system efficiencies are typically in the 70-80% range.

60% is feasible for e.g. nuclear and gas, if you use more than one turbine and there is a big constant temperature differential. This typically isn't the case for gas plants which are intentionally variable and often intended to be cheap to build. While at peak temperature, they might run at peak efficiency around the theoretical maximum of 60% (thermal to electric) with a multi-turbine assembly, typically efficiency is far lower because gas plants usually don't run at peak efficiency and only have one turbine.

I don't think that any nuclear reactor has achieved 60% thermal-to-electricity efficiency. In a water cooled reactor the hot side starts with cooler steam than a combustion-fired plant can generate so it's hard to reach really high efficiency. Reactors cooled with helium, molten salts, or liquid metal could theoretically do better but I don't think that any actually-built power reactors have reached 60%.

The brand new EPR achieves only 37% thermal efficiency and that is considered a good number for a power reactor:

https://www.world-nuclear.org/information-library/nuclear-fu...

No, you are right, 60% is a theoretical maximum achievable maybe with supercritical reactor coolant. The actual maximum for existing reactors is somewhere just below 40%.

Keep in mind that pure gas heating is also not 100% efficient because you need to remove the exhaust, meaning you need to use a heat exchanger and no heat exchanger is 100% efficient either. Some of the heat gets carried outside.

Sure but these days even the cheap stuff is around 95% efficient because that enables the use of cheaper plastic exhaust pipes instead of insulated metal.