So total energy consumed isn't what these places are optimizing for. LLNL/NIF "invented" a lot of this research so their facility is the least efficient but probably most important in the world. When they constructed their laser facility in 1996, NIF used the surest-bet laser system acknowledging that hypothetical competing systems could be better suited (solid state lasers were just coming into play at the time due to semiconductor manufacturing). They've done a massive amount of work ramp up the power and get their <0.5% system to ~0.7% efficient (power from the wall:power hitting the target). The NIF facility uses "indirect drive" where the energy from the lasers are first converted to xrays, and then the fuel is energized with the xrays. Not coincidentally, that's the exact mechanism that the Teller-Ulam nuclear warheads use to drive their fusion stage -- so NIF's selection here makes even more sense given their DOD funding.

Since a lot of modern laser research now overlaps with advanced semiconductor manufacturing, the competing systems are much more mature. Here's a good rundown, but experts think that it's plausible to use even up to 20% efficient systems. Rather than using the laser to first generate xrays - these "direct drive" systems deposit the energy from the lasers directly on the pellets.

https://physicstoday.scitation.org/do/10.1063/pt.6.2.2021102...