Well stat wise, both Solgaleo and Lunala are fairly similar as they have the same base stat for HP and Speed. As for the other stats, Solgaleo is your Atk and Def type, with moderately good SpAtk and SpDef, whereas Lunala has the opposite stats, therefore making it better in SpAtk and SpDef and moderately good in Atk and Def. Therefore, your decision should consider moves, weaknesses/resistances, and ability.
To start of, Solgaleo's ability Full Metal Body prevents its stats from being lowered. This has the same effect as Clear Body and White Smoke; so if your a Metagross or Legendary Golem user, and you like this affect, Solgaleo would be a good start in your decision. Solgaleo also has a great amount of resistances as you'd get being a steel-type (9 resistances; 1 immunity), so having this, as well as great defenses, making this Pokemon not easily knocked out. Solgaleo can also learn great STAB moves such as Zen Headbutt and Sunsteel Strike, as well as other powerful physical moves such as Flare Blitz and Earthquake. However, you may want to use it's resistances and defenses and make it a status user, thus giving it moves like Cosmic Power and Noble Roar - and having it's STAB signature move can also be a great addition to this move set.
With Lunala's ability, Shadow Shield, it reduces half the damage when its HP is full. It has the same effect as Dragonite's and Lugia's Multiscale, so you may consider Lunala if you like the way it works with these Pokemon. In terms of resistances, Lunala is fairly good (with 2 resistances and 2 immunities), but it's only 2 weaknesses are 4x as effective, so having it being hit by a physical move can be really catastrophic. Lunala can also learn great STAB moves like Psychic and Moongeist Beam, as well as other powerful special moves such as Hyper Beam, Ice Beam, Moonblast, Night Daze, and Thunderbolt. You may choose Lunala to be a status user by giving it moves like Confuse Ray and Cosmic Power, but there's not enough to make it a good status user.
Overall, both Pokemon in their respective games are great, but for 1v1, I would definitely choose Solgaleo > Lunala, because they are both similar stat wise, plus Solgaleo has more resistances, and still maintaining the same HP, Spd, and amount of its appropriate attack. This way, Solgaleo has a better chance of lasting longer in battle, while still getting the same job done in comparison to Lunala.
Your Choice! Hope I helped! :)