my first instinct is to say PITCH...
personally...even if you're emoting well,,,and have a great "sound" (whether that's crystal clear...or colorful ala Janis or Rod Stewart) if you're off key... I cannot tolerate listening to you for very long.
But with autotune these days... it seems less of a concern (and that's a pity) in which case I'd have to echo Mike... and say a great singer will make you believe that they actually believe what they are singing. I've heard too many singers (very skilled singers) sing like they are thinking about yesterday's dinner dishes and not really connected to the song. show me the appropriate emotion.