Both have their faults. Both have times when they're wrong and the other is right. Each method is imperfect, but they both have their own purpose and both must be used. It would be very ill, academically speaking, to use just one method. With that said, which do you find is more accurate? (overall)
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Both, Ice cores, etc... for pre-human/environmental data, historical accounts for a basic idea of what happened+People's opinions at the time as well as different perspectives on a certain event