When comparing Primecoin vs ZCash, the Slant community recommends ZCash for most people. In the question“What are the best cryptocurrencies?” ZCash is ranked 8th while Primecoin is ranked 17th. The most important reason people chose ZCash is:
ZCash is listed on Coinbase, arguably one of the easiest to use exchanges.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Scientific Research
Helps find more prime numbers. It also helps prove that they are random.
Pro Gets Harder to Mine Over Time
Pro Traded on Coinbase
ZCash is listed on Coinbase, arguably one of the easiest to use exchanges.
Pro Anonymous
Decently Anonymous Cryptocurrency
Cons
Con Traceable
Not anonymous, transactions are easily traced.
Con Trusted Setup
In order to remain anonymous you must utilize a set of keys set by a group of individuals. If it got cracked or somehow leaked or if this group was corrupt your transactions might not be anonymous.
There is discussion to change this: https://www.starkware.co/
More Info: https://www.reddit.com/r/zec/comments/551wnw/what_is_the_trusted_setup_in_zcash_an_overview/