Perhaps I'm oversimplifying, but it seems quite obvious that CAs are around 76% more efficient than BBs in terms of attack capabilities per IC. I'm a bit surprised.
1938 Battleship: 7,300 IC days. 21 Sea Attack.
1938 Heavy Cruiser: 2,170 IC days. 11 Sea Attack.
Thus, 1 BB equals 3.3 CAs. Put another way, 21 Sea Attack versus 37 Sea Attack. Now, I'm not sure about the best way to factor other points of comparison like cumulative sea defense, org, etc, but I'd guess that they go even more heavily in favor of the CA, for reasons similar to the cruizerzerg.
1938 Battleship: 7,300 IC days. 21 Sea Attack.
1938 Heavy Cruiser: 2,170 IC days. 11 Sea Attack.
Thus, 1 BB equals 3.3 CAs. Put another way, 21 Sea Attack versus 37 Sea Attack. Now, I'm not sure about the best way to factor other points of comparison like cumulative sea defense, org, etc, but I'd guess that they go even more heavily in favor of the CA, for reasons similar to the cruizerzerg.