1. Both are adjectives 很调皮/很淘气 调皮的孩子/(淘气的孩子） 2. formal：顽皮 -- 调皮 -- 淘气 ：colloquial 3. 淘气 is seldome used in writing 4. 调皮 is used on more occasions and by more people. Some people never use 淘气, probabally because of its Northern origin.

调皮是中性一些的词，淘气一般用在贬义也可以用于中性。 例如：这小孩子好调皮的，有时太淘气，真让人担心。

For me, i dont see any difference between these two. Both can be used in writing and speaking and again with no much difference at all.