I want the sense that I'm included in the events of the game, not just an outward observer. Most cinematic games with shallow gameplay don't make me feel like I'm involved. Games like Xenosaga, GTA:VC and the first two Metal Gear Solids didn't connect me with the characters in any way, no matter how well the stories were told.
But in GTAIII, San Andreas and MGS3, I have a connection to the character. In GTAIII, I got the sense that people were talking to me. Its a small thing, its as old as Chrono Trigger or Fire Emblem, but I like that. VC tore that away and offered no feeling of roleplay in return. I was just Tommy Vercetti voiced by Ray Liotta, I preferred he just shut the hell up like GTA III Guy.
Enter San Andreas. Like Tommy Vercetti, Carl Johnson has a voice of his own. but I'm given so many ways of determining his skills and appearance that I'm able to get into his role better. Plus the nod to the silent GTA III guy was just classy.
MGS3 has such a great depth and immersion to how it plays that I finally feel like I'm Snake rather than just watching a compilation of cutscenes all the time. Tossing out the radar might have been the best thing for the series. The boss fight with The End in particular was thrilling and the codecs have yet to disrupt the gameplay flow as they did in MGS2.
Even FFX, to a small extent, made you feel like the hero. Tidus' name is never spoken between either FFX game and it generally understood to be you. Still, I like it better in FFXI or KOTOR, where the story feels like all the events fall on me and I'M the hero, not some bystander.
I prefer (1) and not (2) unless it can really excel at making itself feel like (1). I want my ego trip with the $50 dollars I pay to escape into a game. If I wanted to watch someone else's life unfold, I'd just read a bood or go see a movie. I want to interact with my game and should never be watching more than playing.