Winston argues with Julia that they are both "dead," while she disagrees with this stating, "... I'm alive!" Who is right in your opinion and why?

Winston is correct. Winston knows their days are numbered while Julia feels they can keep meeting together like it is some kind of game where she can outsmart the party. Winston continually says "folly" about what they are doing. Winston is under know illusions that their whole affair is going to be discovered and end very badly.