to get the most BTU out its easy, move the most air!
Assuming that the blowers wont effect what is happening on the inside (they do, but probably not too much, at least on an insert). Then the heat transfer occurs quickest when you have the largest difference between the two items. So in this case, move the most air so that it doesnt heat up as much. moving half the air doesnt mean you are getting half the energy out, as its hotter, but if you move half the air, it wont be twice as hot. (half in volume, not half on the switch either).
In reality, I have an insert, without the blowers I get nearly zero heat out. I run the blower on high full time (its a switch, no speed options). free standing stove owners may disagree. Moving more air will likely heat up a bigger space in your house though, so more losses there, but it will be a bit more uniform. Less volume will mean hotter air that is more prone to go straight to the ceiling. Some people find the movement of the air might me less comfortable, so it may feel different too. higher fan speeds are going to extract more heat, but it might not be a clear winner depending on lots of variables.
Once the fire is going well, if I turn on the blower, I cant say that i see a difference in the firebox. The temperature reading of the stove will drop! But that is because you are cooling the metal from the surface in. So if your surface thermometer says 700F with the blowers off, the inside of the box isnot the same as if it says 700F with the blowers on... but you dont care since its the steel you are worried about. Since the blowers on high will pull out, say 20% more btu (just a guess), that btu is coming from the inside of the box. How that effects the burn will depend on many things (stove design, wood type, etc).
At the end. The arm load of wood you toss into the stove has a certain number of BTU, the stove can only be so efficient (usually low 70%, mine I think is 72%). after that its a question of how efficient you are operating it, and if you are trying to get all the BTU now, or have a slower fire and drag it out.