In Reg I, why is Solgaleo usually outclassed by Ho-Oh and Lunala? What can they do that Solgaleo can't?
Solgaleo and Lunala have a lot in common, however the reason Lunala is used is nothing regulation specific. Firstly, Lunala is better offensively speaking than Solgaleo. Ghost-STAB is much more valuable and spammable than Solgaleo’s Steel-STAB. There are better Psychic-type moves on the special side (expanding force, psychic, psyshock) than on the physical side (zen headbutt, psychic fangs. Additionally, Solgaleo has no comparable coverage move to Meteor Beam, which is like a really good move and allows it to OHKO incineroar. There are options like Close Combat and Earthquake, but these have their drawbacks, and simply aren’t as strong. In terms of support, both Solgaleo and Lunala have some really good options (namely Trick Room and Wide Guard). You may be inclined to think that Solgaleo is a better abuser of these moves, as it has better defensive typing. However, Lunala has an amazing defensive ability in Shadow Shield (Clear Body is good offensively for Solgaleo as it blocks intimidate, but this just puts it on ‘level-footing’ with Lunala, who also is not vulnerable to intimidate). Shadow shield is like really really good!!! As important is the fact that Lunala is immune to Fake Out. Both these facts are important on this Pokémon specifically, as it means you are not forced to run protect, which helps with Lunala’s 4 move syndrome (when a Pokémon wants to run more than 4 moves). Solgaleo also wants to run more than 4 moves. However, it also REALLY wants to run protect, to get around Fake Out, and to avoid dying to strong double ups. If you try and think about what 4 moves you can run on Solgaleo, you are constantly running into issues. If you have to run protect, do you drop Trick Room or Wide Guard? Which offensive moves do you run? A steel move and Close Combat? That just sounds like a bad Zamazenta! A psychic move and Close Combat? That does not sound scary at all!
TLDR: Solgaleo is both worse at dealing damage and supporting its team than Lunala! It is completely outclassed.
Ho-Oh and Solgaleo aren’t really comparably Pokémon, but what I will say is that Ho-Oh is used due to the context of the meta. It has good synergy with Miraidon which I can talk about if your interested, and is a decent restricted sun abuser as a natural fire type not named Reshiram. It also helps that rock type moves are not common at all.