Definitely BODs.
Unlike fighting creatures (where fame is subject to diminishing returns, as you get closer to the fame level of the creature fought), BODs give the same amount of fame whether you're currently 0 Fame or 10,000 Fame.
BODs give fame as follows:
1. Find the point value of the BOD in the system.
2. Divide that number by 50, round down.
3. Square the result.
So, Tailor BODs can give as little as 0 (anything 10 or 15 count normal cloth or leather) to as much as 256 fame (20 count EX Barbed 6-part LBOD).
Smith BODs are worth more, though like cloth, iron normal smalls under 20 count are worthless. Smalls can be worth up to 256 fame (a Valorite EX 20 Small), and of course 11 of 24 armor/shield/helm BODs are the non-combinable types making almost 25% of your BODs candidates for turning in as smalls before you even consult the charts to see if using in an LBOD would be worth the reward. Larges start at 16 fame (for a 10 or 15 count normal iron ringmail or polearm LBOD), up to (I think) 576 (24 squared) for a 20 EX Valorite Plate LBOD.
I believe the smith BODs that have a chance to give POF are in the 16 to 25 Fame range, so by farming your own POF through BOD filling, you can thousands of fame very quickly, with no combat risk.