Hi jalexandratos. I don't think a lot of conversion would be necessary to run a BX/OSE module. I would say HoA is designed to be a bit more low powered and low magic as a general principle but no reason why you couldn't run other adventures. If I was converting an adventure I would focus on the following areas:

• Stats: Hit Points = Health, Armour Class = Defence, Base Attack Bonus = Skill Die. Use the Heroes of Adventure equivalents or convert as follows:
  • Convert AC to ascending Armour Class = Defence score
  • For every 1HD = +5 health
  • Convert Base Attack Bonus to a skill die (+1 = d4, +2 = d6, +3 = d8)
  • Damage rolls = no change
• Balancing = You could not worry about it (it's OSR, people may have to run away from time to time) or just vary the number or condition of monsters (i.e. if the adventure says 4 Ogres are present then make it 1 or 2 for example).
• Monetary system = Default is silver pieces in Heroes of Adventure
• XP = Could use as is or simply adopt a milestone system (i.e. level up after each adventure)

This hasn't been fully tested so would expect the referee to adjust as needed but it would be my starting point.