I have heard that there is one, and Ho-oh and Lugia star in it, clashing against each other.
Also, Ho-oh would win. I am not saying this because I like him more, but its proven. Lugia has really bad Defense, so a Sacred Fire would do way more damage than an Aeroblast or Hydro Pump. Its been proven, Ho-oh takes Lugia's HP down to the yellow with a Normal Effective move, while Lugia doesnt with a move that is Super Effevtive against Ho-Oh.
I'd really like to know where you pull out these supposedly proven facts of yours. (I have a pretty good hunch, but I won't go there) Lugia's base stats in HP, Defense and Special Defense are 106, 130 and 154 respectively. These are some pretty high stats even on Uber standards. Your comparison also fails to take into account factors such as:
Typing
Movepool
Viability in the Uber metagame in general
Stealth Rock damage (Lugia's 25% switch-in damage versus Ho-oh's 50%)
And most importantly, you're assuming that both players are merely throwing strong offensive moves at each other. Lugia is most commonly used as a wall (and a damn good one, even though its Defense is "proven to be bad") and with its higher base Speed, Lugia can use Toxic, set up Reflect and proceed to stall Ho-oh out of Sacred Fires while it's fainting from Toxic. Even with Sacred Fire's incredible Burn rate, I doubt Ho-oh could beat Lugia without getting lucky with critical hits.
Even if Ho-oh would beat Lugia more often than not, it tells us nothing about which one is better in general. Pokémon is not a 1-on-1 game so when comparing two Pokémon, it should not be treated as such. Ho-oh is not only crippled by its 4x weakness to Stealth Rock, but it's just asking for Palkia to come in and wreak havoc and gets royally screwed over by Kyogre as well. In terms of sweeping, it's physically outclassed in many ways by Rayquaza and Groudon and as a special sweeper, it's stopped right in its tracks by Blissey, something many of the other special sweepers in Ubers can deal with despite its massive HP and Special Defense. Defensively, I'd say Lugia is better despite those nasty weaknesses to Ghost and Ice that Ho-oh lacks. I'd really want Ho-oh to be usable and to be fair, it's not utterly terrible, but with the amount of Pokémon in the Uber metagame that are resistant to Fire, it just gives too many opportunities for some of the nastiest threats in Ubers to come in.
That said, I obviously prefer Lugia in terms of usefulness. As for design, I really like Ho-oh, but I'd have to say Lugia wins in that department, too.
