Saigo is much more commonly used.
To get some feeling for how they're used, look at the example sentences in a good J/E dictionary.
For example,
saigo http://dic.yahoo.co.jp/dsearch?enc=UTF-8&p=%E6%9C%80%E5%BE%8C&stype=0&dtype=3
saishuu http://dic.yahoo.co.jp/dsearch?enc=UTF-8&p=%E6%9C%80%E7%B5%82&stype=0&dtype=3
Alternatively, if you're not sure, then use 'saigo'.
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