Ok, they are pretty equal is Speed and AP.
Both are IC, but since they pratically hate each other in lore, i think that this is not a disavantage.
Their moveset are also pretty similar, with only 4 attacks that differ, but Lugia has more attacks by events. Lugia also has a way better item than Ho-Oh, that being Leftovers over Sacred Ash.
Both have Calm Mind anf Future Sight, however, Lugia can have the Speed via Tailwind, so that is nice. The abilities are different to say the least, while Multiscale is a better start Ability, Regenerator can really do alot, but since they know each other, i doubt that Lugia will use Whirlwind. Both can make use of the move Punishment to punish them for spamming Calm Mind, but that would be better for Ho-Oh due to Lugia being type Psychic. About the super effective moves, Lugia seems to be better in this regard, with Hydro Pump and Ancient Power, however, after Burn Up, Ho-Oh would lose this weakness, and since they know each other, i can see he using that to get rid of problematic things, although he would lose Stab on alot of good moves. Lugia has better healing because of Leftovers, both have Recover, so that is nice. There is also the Weather Wars, Rain Dance would screw with most attacks of Ho-Oh, but he could just use Weather Ball with no downside, Sunny Day don't hurt Lugia alot, since he still has Aeroblast, but the guy would not just let the Ho-Oh with a boost in strenght, and Lugia can't spam Weather Ball like Ho-Oh.
This battle can go on so much ways, since both have prior knowledge about each other, and they can try to counter them, while Lugia has Tailwind, this could just let Ho-Oh to set up a free Calm Mind, and since all of Lugia's attacks are Special, that will kinda suck for him, but Ho-Oh has good moves on both spectrum. There are alot of possibilities for this that each one has a split chance to win.
I will vote Incon due to they knowing each other so well that this can go on many ways
