For a game based on "Dungeons & Dragons", I don't get the chance to throw too many dragons at my players. Since the players fought and defeated a white dragon statted like one from the Moldvay Basic book last week, I was able to make some observations.
Encounters with dragons are dangerous and random. The dragon will open the fight with a breath weapon, and there's a 50% chance it will breath each round thereafter (max of 3 times per day). A healthy 40hp dragon, breathing 3 times in a row, would wipe out almost any mid-level party (120 damage!) Alternatively, if the DM doesn't roll the 50% chance, the dragon might not get the chance to breath again all fight. As I said - the randomness of the breath weapon make it dangerous, and random.
Another factor is that the dragon's breath damage is tied to its current hit points. If a party hits it hard, with a lot of early damage, they can greatly reduce the threat of the breath weapon. In our game, the players ditched in a side passage, letting an automaton they were controlling engage the dragon, until they could launch an effective bum rush, knocking the dragon out of its high hit points with some solid swings (which allowed them to survive the remaining two breath attacks when they finally came).
As the DM, I wasn't happy with the 50% chance of breathing; my dice were cold and it didn't breath until late in the fight, when its hit point total was greatly reduced. But I do understand the need to reign in the overwhelming breath attack with the variability so a party isn't overwhelmed in 3 rounds of breath attacks.
The BX white dragon attacks with two claws and a bite (damage 1-4/1-4/2-16) and has only 6 HD. That makes it a glass cannon - the opening breath is really threatening, the physical attacks aren't fantastic, and the remaining breaths are the mercy of the dice.
Since I wasn't terribly impressed with the BX version, I checked out how the white dragon fared in some of the other rules that frequent my table.
The white dragon in the 1E AD&D monster manual is exactly the same statistically as the BX version, with one important difference: dragon fear. In AD&D, dragons generate terror which forces lower level characters to flee or take attack penalties. The Black City group wouldn't have struggled against the AD&D version - they had too many 1st or 2nd level retainers or replacement characters that would have fled.
BECMI / Rules Cyclopedia
The Mentzer set, and the Rules Cyclopedia, had a major problem because they stretched play over 36 levels - how do you scale dragons to threaten characters over such a long career? The BX dragons were re-branded as "small dragons", and large and huge variants were added (9 and 12 HD respectively, for the white dragon, with rules to bump the HD even further). The requirement of rolling a 50% chance for breathing was removed for the large and huge dragons, tacitly allowing the DM to use the breath to do the most harm each round. The larger dragons are also given some additional combat options (swooping dives, crushes, kicks, tail sweeps, and so forth).
Adventurer Conqueror King (ACKS)
The dragon hierarchy is flattened in ACKS, so that any adult dragon will have 10 HD regardless of color. The breath weapon is 1d6 per hit die, decoupling it from the dragon's hit points but keeping a variable factor - which means that even an injured dragon can uncork a ferocious breath attack of 10d6 damage. ACKS does keep the 50% chance of breathing each round that you see in BX or AD&D (max of 3 per day). One of the real interesting things is giving each dragon a special offensive or defensive ability, like invulnerability, gem-encrusted hide, decapitating bite, and so forth, making each dragon encounter memorable and more dangerous.
I'm really happy with the uptick in danger represented by the ACKS dragons - any adult dragon is a house, the late-fight breath weapon is still devastating, the ancient dragons are as dangerous as the BECMI huge dragons, and the new special abilities are flavorful and interesting.