There's hardly a way to objectively describe why a certain scene is "more sad" than others. If the Lion King's your cup of tea, why not spill some tears there. If you like "24", things might be different for you personally.*
Transported emotion and the visuals of a game are, however, very connected. If you don't like the graphic portrayal of the characters, there's hardly a way to make the story really moving for you. Yet in the Law & Order series, actors did not really seem to display their emotions so openly. Facial expression did not play that much of a role for Vincent D'Onofrio or Ice-T at least.
* Disclaimer: I've only watched half the first season of "24" and I considered the naivety with which this show was written to be quite, quite comparable to The Lion King. I then suffered from cliché overload, and when I finally thought "one more cliché and I'm out of that series", one of the characters suddenly suffered from amnesia. So that was my little 24 story, while we're being off topic.