head to head
Neither is harder. They score identically on all four axes, so the difference between them is in kind, not degree.

Optimization · Pure Optimization
The 2002 Total War pairing turn-based medieval empire management with massive real-time battles.

Optimization · Pure Optimization
A strategy wargame pairing turn-based management of feudal Japan with real-time mass battles.
Medieval: Total War leans Optimization (Pure Optimization); Shogun: Total War leans Optimization (Pure Optimization).
Same score on execution - which means the number cannot separate them. The difference is in what each one asks of you.
Medieval: Total War
Real-time battle control rewards quick unit handling
Shogun: Total War
Real-time battle micro matters but pace is forgiving
Same score on reads - which means the number cannot separate them. The difference is in what each one asks of you.
Medieval: Total War
Multiplayer battles add human feints; campaign AI is scripted
Shogun: Total War
Campaign AI daimyos follow mappable behaviors
Same score on variance - which means the number cannot separate them. The difference is in what each one asks of you.
Medieval: Total War
Battle dice, loyalty and event cards add noise
Shogun: Total War
Fog of war and agent rolls hide information
Same score on optimization - which means the number cannot separate them. The difference is in what each one asks of you.
Medieval: Total War
Campaign economy and battlefield doctrine are deeply learnable
Shogun: Total War
Campaign economy, army composition and terrain 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.