The point was that she tried to resist it, which was what made her different than other people Lulu had Geass'ed. Perhaps it was because of Lulu's Geass being disrupted by V.V.'s trap or perhaps it was because of Euphie's strong will, but she was one of the only to resist the power. I liken her strong will to the workings of the Death Note, because the task of killing innocent people was practically impossible to Euphie, which might have been the reason for her resisitance. That she failed in the end doesn't much matter (though, I would point out that she does overcome the Geass at the end of her life, because she does not want to kill the guy she loves: Suzaku).
And should the girl have died/be in a coma/etc because of her attempt to do her job, I think that would actually be more of a reason for the Geass and the Death Note to be similar.
Finally, I think it should be mentioned that Euphie died while trying to kill all the Japanese. Even if Lelouch hadn't shot her, she would never have been physically able to kill all the Japanese. Eventually, she would probably have been stopped by someone else, and then died trying to escape. At least, in my mind anyway...
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And should the girl have died/be in a coma/etc because of her attempt to do her job, I think that would actually be more of a reason for the Geass and the Death Note to be similar.
Finally, I think it should be mentioned that Euphie died while trying to kill all the Japanese. Even if Lelouch hadn't shot her, she would never have been physically able to kill all the Japanese. Eventually, she would probably have been stopped by someone else, and then died trying to escape. At least, in my mind anyway...