The level of anonymity in ZCASH is, unfortunotely, not very high.  It could *potentially* be very high, but because of the fact that ZCASH is not enforcing anonymity, and people are not using it much in "anonymous mode", the ACTUAL anonymity set offered by ZCASH (namely, those people using the anonymous mode) is pretty small.

For the moment, monero is by far more anonymous in practice than ZCASH.   This is because even though the *initial* anonymity set of monero is relatively small, it grows over time, and monero has already a significant user base which ultimately is the anonymity set.

ZCASH uses better anonymity crypto (in principle), namely ZK proofs, but fucks it up by not imposing it on everybody all the time.

Monero uses ring signatures, which start out with a small anonymity set (but drawn from a much larger pool) and increases this set over time (each time your address is drawn for another transaction somewhere).