Does the "Procurer" and "Retriever" mining barges have the same yield?
Solution 1:
These mining barges serve different purposes.
The Procurer is massively more durable than the retriever. It has far more armor, shield, etc (and a Mining Barge skill bonus to shields) which make it idea for situations where defense might matter (suicide ganks in high sec, wormhole mining, etc).
The retriever is very flimsy, but has double the ore-hold, reducing the number of trips back to station.
From a yield perspective, looking at regular mining, they are basically the same:
Where X is 1 normal strip miner: Procurer: 1 turret @ 300% = 3X Retriever: 2 turrets @ 150% = 3X The retriever has 1 extra low slot, which might increase the yield slightly through mining upgrades.
Effective Hit Points (EHP): Procurer: 5500 + 5000 + (6000 * 1.25) = 18000 (also 4 med slots = much greater shield tank) Retriever: 2000 + 1700 + 2300 = 6000 (with only 1 mid slot!)
Cargo: Retriever: 22000 * 1.25 = 27500 m3 Procurer: 12000 m3
I think the above summarizes the tradeoffs. The mining yeild is very similar - but defense vs cargo space is really the decision making factor.