I should correct my last post I meant to say 'discharge rate vs capacity'
Generally speaking I would look for IMR cells but I would also still pay attention to the specs. One of the links I gave is for AW IMR cells which are highly revered in other circles because it boasts +15A current. The second link is for panasonic cells which boast 10A current with marginally longer run time.
There are many other batteries that claim all sorts of things but if you stick with trusted brands the specs should be reasonably accurate (sounds familiar doesn't it).
If you really want to satisfy your puzzle about your recent upgrade you could connect the battery pack to a cordless drill using wires and an watt meter in series. Pull the trigger and add a little resistance to the drill (maybe put a glove on) then watch how many amps are pulled and volts dropped. Repeat with the stock battery and compare results.
Crude? Yes, very crude but it should be kinda easy to tell the difference between 3A cells and 10A cells.