The Difference in Mining with Multiple Rigs between Bitcoin and Zcash

[ethereal1m]

Hello,
I try to understand how the mining hardware environment is different between Bitcoin when centralized mining ecosystem is more encouraged compare to Zcash or Ethereum where pooling is more encouraged.

So is it true that when you have 2 separate rigs mining bitcoins, each individually not joining a pool, they could compete with each other, as oppose to mining Zcash or Ethereum, the 2 rigs join forces to mine together
in the same pool?

regards