Hoax, sadly, without any offense to you. This reported capacity doesn't have anything to do with real one.

BME Alternative is, in fact, taking voltage report from BME, and appending dr_frost_dk's algorithm to calculate remaining % of charge. If doesn't have anything to do with capacity readings (mAh), and probably, you got this 660mAh/710mAh due to resistor between BMI and battery (-). This particular battery must use strange one, there, instead of 100kOhm regular.
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What I suspect, is that it's - at best - regular 1300 mAh one. It gives good results, compare to your old battery, which must have low amount of capacity left at max (probably, real is less than 1000).
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If, by any chance,you're interesting in measuring capacity of your new battery in reliable way, see my signature - one of links there forward you to instruction, how to do it on-device, using bq27x00 chip, present on N900.

/Estel