Most Sandbox roleplays are inevitably going too be character-driven, because there's little plot to speak of except the backstory, and one that spawns from the player character's own initiative. That said, the appeal of sandbox RPs can be summarized as:
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[*]Exploration of the given setting.
[*]Interaction between different player characters. 
[*]Character development, which is arguably one of the ultimate goals there is in a sandbox RP.
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Being character-driven, it's terribly important for sandbox PCs to be more fleshed out. They generally have long backstories and thorough, deep personalities. While a story-driven fantasy RP will have you pondering which skillset is the best for your odds of being awesome, a character-driven cyberpunk RP will have you thinking more on what motivates your character, what caused them to think and see the world like they do, and (perhaps most excitingly) the various possibilities they can develop into; basically making your character 'fun' to interact with. This is the backbone of a sandbox RP, and the reason why such RPs filled with tragic broody loner characters die faster than you can say 'Fonz'.

Still, I found one aspect often neglected in sandbox RPs: A stopping point. Odd as it may seem, the maturation of your character's personality provides a degree of closure, but not enough to conclude the RP from a collaborative writing standpoint. 'Graduation' is the logical stopping point for sandbox school RPs, a conclusion most never saw. 'Start of the War' is the stopping point of an old fantasy military base sandbox RP I was part of in the oldguild (the fates of the characters left ambiguous).

When you look back through the various conversations, swordfights, and interactions that made your character way more than what they were when you first posted their character sheets, you know that the sandbox RP you participated in was worth it.