Halo 3 Multiplayer is marvelously cinematic, but the Campaign was awkwardly plotted and overly linear compared to Halo: Combat Evolved, where the combat really did feel 'evolved'.
Call of Duty 4 is the reverse. Immersive campaign with lots of interesting cinematic set pieces creating true variety in the gameplay, whilst the overly desaturated khaki-coloured multiplayer maps and awkward controls spoil the sense of empowerment.
However, that is just FPSes. Obviously, one needs to ask why Super Mario 64 is better than other 3D platformers that have come since.
We know what are the good games, so what unifies them? I have a fair idea, but it would take too long to go into now.
Personally, I think that Controls are the most important aspect and should be designed with a view to overcome the disability the gamepad imposes on the player and allow them to feel that they can competently control their in-game avatar. This leads to empowerment. If this over-balances the game in the player's favor (i.e. making headshots too easy in Goldeneye 007 due to its 'floating gunsight' in Aim mode) the game should re-balance the game by throwing more enemies at the player.
Conversely, I think that Story is the least important aspect, but it troubles me that much of this new generation of games seems to be made by developers who really wish they had gone to film school. If I want a narrative I will passively watch one that is well acted and edited. This will be an immersive experience where I am happy to suspend disbelief and partake of an emotionally and intellectually stimulating escape. Although, I can appreciate why games increasingly tell stories these days I feel that it is the marketing departments of publishers who have come to the conclusion that you can promote something if it looks vaguely like a Hollywood blockbuster, talk about its hero, pitch its high-concept in a TV advert, even if you have little or no idea what the actual game would be like to play. These publishers then force developers to fit a game around this narrative, trying to shoe-horn in as many cinematic set-pieces as possible, or just do them as cut-scenes. This results in products that have 'undifferentiated' gorgeous lighting, specially composed orchestral 'contextual' music and incidental 'random' dialogue from its "extras" whilst retaining interaction ergo 'gameplay', but not necessarily fun.
Most games these days are so overburdened by the weight of presentation and restrictions of narrative that it becomes impossible to create: worlds of artificial life in which the player can feel empowerment, experience discovery and exercise choice.