It's tough to choose one actually. Ho-Oh has decent ranged and melee attacks, though it's strongest moves usually have downsides like taking recoil damage or losing the fire type temporarily. I think a big decider here will be what ability Ho-Oh has. Pressure ensures or at least helps Ho-Oh in a battle of attrition, which this will likely come down to, but Regenerator is less useful since spending time away from the battle allows Houou to heal as well. Houou's healing states it restores a lot of health, so it's fair to assume it can at least match Ho-Oh's regenerator. If Ho-Oh is too slow or can't find cover while fleeing, it would also leave itself open to Houou's plethora of ranged attacks. I suppose it's also possible that we treat Ho-Oh as having both here.
Houou having a counter to ranged moves also helps it a lot here, since Ho-Oh will be forced to either find a way around it, which would most likely be resorting to melee. Being unable, or having more difficulty, fighting at range means that Ho-Oh will take more hits to start, as an entire section of it's arsenal is essentially worthless unless it can misdirect Houou or cause it to drop it's guard long enough for a ranged move to hit. Absorbing life force is also quite handy for Houou here, since it can passively damage Ho-Oh without being too aggressive so as to leave an opening, and it being energy based likely means it works at range as well so it wouldn't need to enter Ho-Oh's active range to do so.
Houou also has access to powerful light attacks, that Ho-Oh won't be resisting, a buff to said light attacks, and a potential instant kill. If push comes to shove Houou even has Safety Guard to prevent it's defeat, and with it's healing it can potentially come back from a near-loss fairly easily unless it's caught off-guard.
Overall if I had to vote now I'd guess Houou would win since it has a wide array of moves that include healing, buffs, guarding itself from death, instant death, absorbing life force, and just generally powerful attacks. It's worth noting that moves like Extrasensory would get around Houou's ranged barrier, but Houou's resistance to mind/soul attacks and the fact all it's own attacks hit the mind/soul make this seem pretty decisive. Both have healing, but Houou will defend against ranged attacks while counter attacking from the same range so healing works less as supportive evidence for Ho-Oh and more as a balancer for the fight. It's also unknown if Recover can restore the mind/soul damage Houou will be dealing, so I don't see Ho-Oh winning this.
Conclusion. It's hard fought, but Houou eventually wins. Ho-Oh has some chances here but it's advantages aren't as numerous or conclusive as Houou's so it's fighting an uphill battle against an opponent with equal stats, a counter to a lot of it's moves, fairly potent healing, specific damage buffs, and an instant kill. It's also worth noting that Houou isn't helpless in melee range either, since it inherits a few moves from Garudamon that utilize it's talons. My vote should be firmly in favour of Hououmon, unless there's something I missed.
As for the design aspect I'll admit I'm biased toward Ho-Oh a bit, since it's the legendary of my first Pokemon game and I never used Hououmon in any of the Digimon games I played.
Edit: I said "here" so many times that it's painful to read
