head to head
Medieval: Total WarvsThe Settlers: Heritage of Kings
Medieval: Total War leans Optimization (Pure Optimization); The Settlers: Heritage of Kings leans Optimization (Pure Optimization).
Medieval: Total WarThe Settlers: Heritage of Kings
Axis by axis
Execution3 vs 2
Medieval: Total War leans harder on execution: Real-time battle control rewards quick unit handling
Reads2 vs 3
The Settlers: Heritage of Kings leans harder on reads: Multiplayer adds light human prediction; campaign is scripted
Variance3 vs 3
Even - both lean on variance about the same.
Optimization8 vs 8
Even - both lean on optimization about the same.
Two games can score the same on an axis and still test it in very different ways - read each rationale, not just the number.

