Note that there may be some difference in the AAAA sold as a cell and the AAAA used in a pack - typically the Cell by itself has a button on top to press against the light or the next cell , while the AAAA interior lights have a flatop where a strip is spot welded. Also - take note as to the insulation on the 9V vs AAAA cell wall insulation - I'm not honestly sure which is better, but they are different (no bunny logo on it to begin with!)
I also take apart the 9V, but mainly to get the round connectors to use in making surfire rechargable prototypes (they use that exact connector at the top of their batteries - no way to buy it commercially except to tear open a 9V and cut it out.