Ecash seems like a single anonymity set because you can freely transfer in and out of mints using Lightning. i.e make a deposit to one mint, then transfer to one or more other mints. If sats can seamlessly and privately flow throughout all mints then it appears to me that they share the larger anonymity set. Unless I’m missing something, it seems receiving ecash would be the same as receiving monero.

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Tokens are unique to each mint. Every time you leave a mint over lightning you reveal amount + destination to the original mint (a potential point of de-anonymization/reduced anonymity). You're also narrowing down your anon set the larger value of tokens you hold (ecash tokens have "buckets" of 1,2,4,8,16, 32...etc, increasingly fewer denominations exist the larger the bucket)