I went and tested myself; the special side is stronger (you can do it yourself on https://pokemonshowdown.com/damagecalc/
252 SpA Sheer Force Landorus Earth Power vs. 0 HP / 0 SpD Arceus: 151-178 (39.6 - 46.7%) -- guaranteed 3HKO
252 Atk Landorus Earthquake vs. 0 HP / 0 Def Arceus: 136-162 (35.6 - 42.5%) -- guaranteed 3HKO
Earth Power does not have a base power of 120 when combined with Sheer Force, the calculation happens a bit differently. The page at https://bulbapedia.bulbagarden.net/wiki/Damage#Damage_calculation
goes more in-depth on the process, which is too long-winded to describe here. Regardless, the above calcs show the 20 hypothetical base power points matter more than Landorus’s stats.
I don’t see how level up moves should limit what kind of attacker the Pokémon should be. The only thing that matters is which is more effective — as above, the special side is more effective. I’ve articulated before why I believe the special side has a better movepool also, chiefly due to Hidden Power.
Thrash is Normal-type and offers hardly any coverage for Nidoking and is thus subpar. Megahorn suffers for a similar reason, Bug isn’t a great offensive typing. Sheer Force is better on Nidoking’s special side, because it affects moves like Sludge Wave, Earth Power and Ice Beam, and does not affect Nidoking’s main physical attack Earthquake. The same calculator will show that Nidoking’s Earth Power is stronger than its Earthquake using the same fair 252 EV spreads.
I do not believe for a second that you have never seen a special Landorus-I. These stats collected by Smogon show that 99% of high-ranked players in doubles OU use Earth Power on Landorus-I, and 96% use Sheer Force. You can find the numbers with Ctrl+G, though it takes some time to find Incarnate form’s listing. http://www.smogon.com/stats/2017-10/moveset/gen7doublesou-1825.txt
This has turned into a mess so I’m not going to respond any further. I’ve presented my reasoning and I’ve given hard stats, I’m done now.