head to head
Neither is meaningfully harder - they pose close to the same test. The widest gap is execution, and it is a single point.

Execution · Competitive PvP
Large-scale modern combined-arms shooter built on destructible maps and squad teamwork.

Execution · Pure Mechanics
The sequel that built console online multiplayer around ranked Battle Rifle duels.
Battlefield 3 leans Execution (Competitive PvP); Halo 2 leans Execution (Pure Mechanics).
Halo 2 leans a little harder on execution, though the gap is small.
Battlefield 3
Gunplay, suppression management, and vehicle piloting
Halo 2
BR precision and movement tricks online
Same score on reads - which means the number cannot separate them. The difference is in what each one asks of you.
Battlefield 3
Human teams adapt routes and armor pushes
Halo 2
Ranked duels hinge on outplaying humans
Battlefield 3 leans a little harder on variance, though the gap is small.
Battlefield 3
Spawns, destruction, and vehicle drops shuffle engagements
Halo 2
Matchmaking opponents and spawns vary
Same score on optimization - which means the number cannot separate them. The difference is in what each one asks of you.
Battlefield 3
Unlock paths, class synergy, and map control
Halo 2
Map control, timers, and weapon spawns
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.