Last I checked virtually none of Zcash's transaction used the anonymous payment feature (presumably because the performance of it is very poor).
So it's plausible that monero transactions could practically end up with a larger anonymity set in absolute terms than zcash (especially for current monero, which has CT and a minimum mixin size).
I think it would be more accurate to say that Zcash, has, as a feature, a way to make anonymous payments, but it is rarely used.
>So it's plausible that monero transactions could practically end up with a larger anonymity set in absolute terms than zcash (especially for current monero, which has CT and a minimum mixin size).
No, it isn't. There will always be a transaction graph between accounts, which limits the total number of possible routes between two participants in a trade.
Much of the performance issue comes from a single design decision made in Zerocash: to use SHA-256 for the Merkle tree, PRF, and note commitment hashes. We'll be changing this for the Sapling update.
-- Daira Hopwood (Zcash developer)
I hope my portrayal of the performance issues was appropriate.
Yes, your portrayal of the performance issues was fine.
https://explorer.zcha.in/statistics/usage
And here historical stats about shielded and unshielded transactions in the most recent 100 blocks over the life of the blockchain so far (about 6 months):
https://explorer.zcha.in/statistics/timeseries?supply=false&...
Note that a big part of the shielded transactions is because coinbases are required by the consensus rules to be shielded when first spent. This was in order to provide a guaranteed privacy-set. If you make a shielded Zcash transaction today there is actually a very large privacy-set of possible previous transactions which could be inputs to your transaction.
In the long run we intend to improve the functionality of Zcash shielded addresses and to deprecate Zcash transparent addresses, so that all transactions are shielded and so that the user experience is simpler.