A feast of the doctrine that organises every other feast beats a feast of the instrument, though the Cross has the better paradox.
The Cross is apostolic and universal; Corpus Christi is a thirteenth-century Latin institution answering a thirteenth-century Latin controversy. Age and reach both favour the Cross.
Conception over instrument. The Cross matters because of who was on it, which is settled at the Annunciation.
The Spirit poured out on the Church against the veneration of the instrument of one death.