Generally, おお is for Japanese origin words and だい is for Chinsese origin words. とけい is originaly from a Chinese word 土圭, but it's enough common and treated like a Japanese-origin word, so the kun'yomi おお is used here (and it's read おおどけい because of rendaku).
In a practical way, google search might give you the answer.
おおどけい 約 6,560 件
だいどけい 約 5 件
(The four of them are not for "大時計" (巨大時計, 円天符台時計, 邪魔だい。どけい(=退け)、芋侍, 邪魔だい!!どけい~), and the rest one says that だいどけい is a misread.)
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