Eileen can double. If she crits with a physical during a double, Rinoa is going boom. Doesn't hurt that Eileen can cast Copper Flesh a lot.
Ahh, well, there is that... BUT A WELL TIMED LEVIATHAN COULD ACT AS A SHIELD FOR THE DOUBLE!?
Yeah, alright, I see why some are favouring Eileen now. ;p
EDIT: On second though, I'd still see Rinoa as being in higher favor of winning. Her Spirit can be ridiculous if she equips the boosts from Leviathan, and Eileen's only got 4 Earthquakes to play around with. Eileen's also only got a 16% crit rate, and she isn't -that- much faster than Rinoa. Rinoa's HP is crap, but she takes magic very well.
EDIT2: Well, looks like Eileen actually might be able to outlast. With 18 turns of invicibility, thanks to 6 charges of Copper Flesh, and if she spreads them out well enough as to not get killed, she can actually kill Rinoa with a crit on a double, which takes 21 turns to happen... Eileen, you whore.