It's kind of hard to compare, especially since I don't know what you mean by precision: the metrics on both projects are very different.
LIGO is all about minimizing losses as the laser light bounces back and forth the two mirrors. The losses here arise from the stack of materials that the mirrors are made out of, which are multilayers of different oxides plus/minus Si or Ge, I forget. So one metric of course is the surface roughness of the material, but then there are also energetic defects called two-level systems in which atoms can absorb a little bit of light to tunnel into another location and thus contribute to the losses by having absorbed laser energy. There's coefficients of thermal expansion, stresses, that all have to be taken into account and tested as you layer all these dissimilar materials that may behave ok at room temperature but not at cryogenic ones for instance.
So LIGO is a game of minimizing losses, because you're after detecting the faintest of signals: a gravitational wave. Their game is all about increasing the signal to noise ratio.
NIF is a monster of energy. There's the whole steering of an enormous laser pulse which is the addition of 192 beams that have to converge into a tiny area the size of a pencil eraser. There's the containment of all this energy into a steel capsule that looks like something out of a sci-fi piece. There's the manufacture of the 2 mm diameter capsule that starts as plastic but is then coated with diamond, beryllium or more plastic and that leads to inherent asymmetries because it's not easy to coat a non-planar geometry. Already this coating assymmetry is very likely to lead to the hydrodynamic instabilities (https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Taylor_instab...) that are obstructing the path forward. The hole with which you fill up the capsule with DT is still a problem, but they try to sweep it under the rug. The surface roughness of the capsule is a problem, contaminants in the diamond or plastic is a problem, a few atomic percent is enough to significantly dampen the amount of X-ray absorption/transmission. Control of the material's density is another one. The work that goes on all of this is tricky because you can solve all of these and control them very well on a planar geometry, but the moment you want to take this onto a sphere it doesn't work as well, we cannot suspend something in Earth's gravity without using a string, which then introduces an asymmetry. So the best we use is we roll the sphere around, and it's not very good for the tolerances that the scientists think we need.
And NIF has a history of escalation. We are currently shooting 1.6 - 1.8 MJ, but the scientists' simulations had predicted kJ range shots in the beginning, and the estimate has continued to climb. You see it in the article itself that they're hoping to get funding to go to 3 MJ. But there are some studies (Halite-Centurion IIRC) from the 50s that showed you needed like 100 MJ to get inertial confinement fusion on a capsule, and I think we've been happily disregarding those results, because, well, politics, job-protection etc. It's a complicated story, shrouded in a lot of secrecy, so I'm glad to read that the NNSA is reviewing it.
So, precision in LIGO, I don't think translates to precision in NIF. LIGO feels more like golf, NIF feels, like some beasts fighting it out. Very different set of challenges, very different resource pools they can draw from (I would argue that NIF can draw more money but less talent because of security clearance requirements restricting employees to be US citizens).