I’m usually only concerned with user privacy and not miner privacy. For user privacy the infrastructure requirements don’t matter.
Monero’s PoW algorithm is deliberately hard to accelerate on ASIC/FPGA. Zcash’s PoW algorithm was designed to be GPU-friendly, but is now mainly mined on ASICs.
So currently for miner anonymity Monero has the lead.
However, Zcash is planning to move to a hybrid PoW/PoS algorithm and that might change the situation.
Are you concerned with miner privacy?