Webby can surely answer from direct experience, but I can answer from theory and indirect experience. The difference in efficiency will not be noticeable to anyone, comparing a single burn cycle. These numbers are measured as best they can under very specific circumstances, and stove designers test and tune their stoves to achieve the best numbers under these specific circumstances. It may not translate directly to your wood, your install, your house. However, a more efficient stove may burn less wood over the course of an entire heating season, something that is actually measurable by the user.
Now, if the Cod is running full tilt and the Ashford is turned way down, I suspect neither stove will be at 350F. So, I'm not sure I understand the first half of your question. I will say that your house has a given rate of heat loss, for a given outside temperature and wind speed/direction. You need to put BTU's back into the house at a rate similar to the loss, or your house begins to cool. The advantage of a BK is that it simply has a wider range of burn rate, and so you have more control over the rate at which you're putting BTU's back into the house. You correctly assumed there's a fixed number of BTU's in a given load of wood, and all you control is the rate at which they're released, so (minus a small discrepancy in efficiency) both stoves are putting the same overall BTU's back into the house. However, do not forget that your house loses BTU's at a rate proportional to the difference between inside temps and outside temps, so keeping your house at a constant 70 will mean losing slightly less BTU's than cycling up to 75 and letting it fall back down to 70F. If outside temp is 40F, then you're losing BTU's 16% faster at 75F, than you are at a constant 70F [1]. This also have a noticeable effect on yearly wood usage.
[1] - dT = 19.4'K vs. dT = 16.7'K yields 16.2%