head to head
Neither is simply harder - they are hard in different places. Fallout: New Vegas demands more execution; Heroes of Might and Magic III demands more reads.

Optimization · Pure Optimization
A faction-driven RPG-shooter where build and route planning shape every ending.

Optimization · Pure Optimization
Legendary turn-based strategy of castle economies, hero armies, and tile-perfect logistics.
Fallout: New Vegas leans Optimization (Pure Optimization); Heroes of Might and Magic III leans Optimization (Pure Optimization).
Fallout: New Vegas leans clearly harder on execution.
Fallout: New Vegas
Shooter inputs with VATS assist
Heroes of Might and Magic III
Turn-based; zero dexterity
Heroes of Might and Magic III leans clearly harder on reads.
Fallout: New Vegas
Scripted factions and enemies
Heroes of Might and Magic III
Human multiplayer adds bluffing; AI is mappable
Heroes of Might and Magic III leans clearly harder on variance.
Fallout: New Vegas
Some loot and crit RNG
Heroes of Might and Magic III
Map fog, creature banks, and morale rolls
Heroes of Might and Magic III leans a little harder on optimization, though the gap is small.
Fallout: New Vegas
Faction routing, perks, builds heavily rewarded
Heroes of Might and Magic III
Hero chains, build orders, and combat math are deeply solvable
A matching score does not mean a matching test. Two games can both sit at 10 on execution and demand completely different things of you - which is why the reasoning above matters more than the number beside it.