OD&D, by the book, is an inferior game to Advanced Heroquest. My primary sources of complaint are:

• Encumbrance
• The primary modifiers of encumbrance in OD&D are your armor and weapon, and everything else is assumed to weigh 80 gold piece equivalent. The rest of your weight limit is determined entirely by how many gold coins you carry.
• In Heroquest your move speed is modified by armor, and everything else only adds up to your weight limit, until you cannot carry anymore. Again, you are mostly only concerned about how much gold you can carry.
• Gold for XP
• In OD&D, Gold and Monsters both grant XP. In Supplement I: Greyhawk and later, monster XP is trivially small, to the point of not being worth the fight
  
• In AHQ, the only way to level is to pay for training with gold. Monsters also drop gold when they die, such that it can be considered equivalent to an "XP value", however gold has more uses than just as a means to level 
• The Gold feedback loop
• Taken as a whole, the above two points illustrate that both games stress the need to dungeon crawl for gold, but the gold economy and feedback loop is stronger in AHQ 

Further complaints

•  Time tracking by steps-per-turn
• This is much easier to track on a board game with an actual grids or a ruler, than it is to convey and track abstractly in theater of the mind 

• Exploration
• AHQ still allows players the thrill of exploring the unknown
• The method for finding secret doors (actually, generating secret doors) puts more control in the hands of the players while counterbalancing that with a DM's wandering monster check 
• Traps
• AHQ d12 spot and disarm chances make finding several common traps much simpler than OD&D.
•  I like it more than a 2-in-6 for every trap. I also see this as a framework, I can imagine any new trap and give players an X-in-12 chance for finding it. This is assuming that they haven't sussed out the "secret method" planned by the GM of finding and disarming it.
  
  This also straight replaces the Search/Spot/Perception rolls of the d20 system. In fact I think that roll is a flat answer to the problem of finding traps that OD&D has. Importantly, I like the d12 chance because it sets the chance of finding on a per trap basis, and not per character ability score. This is more logical to me and cuts out the need to put a modifier on the perception roll to detect trap.

• Spells
• OD&D Magic-Users know every spell in a spellbook of appropriate level, and can create new spells at the cost of 1,000 gold and a week of research. However, they can only use a limited number per day, and must rest before casting another
• AHQ Wizards also know every spell, however they must roll at the beginning of each round to see if they have enough spell points to cast. This keeps their gameplay dynamic and allows them to be useful more frequently than the OD&D magic-user
• NPCs
• The given NPC Hazard encounters in AHQ are a lot of fun
• Henchmen are easier and less punitive to recruit
• OD&D's morale and loyalty system is better, however
  

For a straight dungeon crawl, AHQ is better than OD&D. What OD&D offers above AHQ is the chance to do more, to journey in the overland and  engage with NPCs. Also maybe build a stronghold and go flying or sailing, but nobody really does that. OD&D shines when you lean into its role as a free-form RPG.

I really do like OD&D and I've run several games with the system, but I've always found it lacking in some pretty big ways and have ended up needing to create many more rulings per session. For a strict dungeon crawl, the more solid rules of AHQ are better for a more enjoyable evening of play.

BONUS:

• No f@#$ing DM 
• AHQ can be played out of the box without a DM, while in OD&D the notion ranges from absurd to plausible with extra procedures and oracles