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

Execution · Pure Mechanics
The sequel that built console online multiplayer around ranked Battle Rifle duels.

Execution · Pure Mechanics
Fast arena-style shooter mixing a scripted Strogg campaign with twitch multiplayer.
Halo 2 leans Execution (Pure Mechanics); Quake 4 leans Execution (Pure Mechanics).
Same score on execution - which means the number cannot separate them. The difference is in what each one asks of you.
Halo 2
BR precision and movement tricks online
Quake 4
Aimbot plus strafe-jump inputs dominate both campaign and multiplayer
Same score on reads - which means the number cannot separate them. The difference is in what each one asks of you.
Halo 2
Ranked duels hinge on outplaying humans
Quake 4
Multiplayer duels reward predicting human positioning and timing
Same score on variance - which means the number cannot separate them. The difference is in what each one asks of you.
Halo 2
Matchmaking opponents and spawns vary
Quake 4
Spawn and item timing add mild uncertainty
Halo 2 leans a little harder on optimization, though the gap is small.
Halo 2
Map control, timers, and weapon spawns
Quake 4
Item control routes and weapon picks are learnable
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.