Leaford has stated that the MF batteries are LiPo (lithium-ion polymer), which is a pretty unique battery technology in e-cigarettes, if what I've read is to be believed. These type batteries are more commonly used in cellphones.
I don't know if the V4L "diamond" batteries are LiPo, but I really don't think the older-tech "standard" V4L batteries are using that tech.
Being LiPo, the BMF batteries come off the charger at 4.23V, fall to 3.7V pretty quickly, and from what I can tell, stay pretty much at 3.7V until a dropoff before the discharge cutoff kicks in and blinks the LED, and the battery delivers no further voltage (LiPo batteries can go as low as 2.7V, but I believe the BMF batteries are cutting off well before that limit is reached). It's really quite remarkable (in my eyes) that they're using this tech in such a sleek enclosure. The battery life speaks for itself.
So, what all that might mean is that the BMF cartos are designed and engineered to work with the tech being used in the BMF battery, and may not be 'compatible' with other batteries, even though the threads are the same.
I'm rambling; I'm sure Leaford can expand.
