So I was trying to gauge how much Passive Income is actually worth so I ran a pretty controlled test. I played my alt in two tabs. On the first tier of gold, it seems passive income 3 only very slightly out paces 1 miner on gold and 1 miner praying.
The bug came when I tried to test the second tier of gold. I mined out the first tier evenly on both sides and garrisoned my miners as they started walking toward the second tier. So with the first tier mined out, I'm equal on both sides. I had put three miners on the statue for mana to be able to click Passive. I did this on both sides as I didn't need to test passive mana again. So I clicked Passive Income 1 on one end and on the other end sent one miner out from the castle. He got there about the same time Passive Income started. As expected, the miner outpaced PI 1.
This is when I found the bug. I wanted the Passive Income side to catch up to the miner side before I started PI 2. To do this, I picked one of the praying miners to mine gold. The miner walked out to the completely full patches of gold and just stood there as if there wasn't any gold. I tried and tried to get him to mine but nope. I garrisoned him and picked another praying miner and same thing. Finally, I picked a garrisoned miner and he did mine.
This happened again on the other end when I tried to get that end caught up with the Passive Income end. The praying miners would not mine gold, but a garrisoned miner would. There were four full patches of gold and one or two or no miners mining in each case.
Incidentally, PI 2 slightly outpaces 1 miner mining the second tier and PI 3 is almost as fast as three miners mining second tier. So that would mean PI 3 is only slightly better than 2 miners early in the game and then is almost as good as 4 miners(3 mining and 1 praying) once the first tier is mined out.
Edit to add: The three miners that I had on mana were three miners over the quota for mining the first tier. And so once the first tier was tapped out, these miners would have been standing around picking their noses anyway had I had all my miners mining, only in this case I had all but one of the other miners garrisoned so it shouldn't have affected the praying miners.