the battery ratings don't take into account discharge rate.
So your newer batteries may have a larger total capacity, but they let go of this energy much quicker.
Rechargeable batteries slowly lose energy the moment they are taken out of the charger, even if you aren't using them, some quicker than others. So a 2500mah battery is not automaticallu better than a 1600mah.
To fix this, you can but a good battery charger that conditions batteries, like the la cross bc900.
Or you can get some of the newer rechargeables that hold their charge a lot longer, such as the eneloops.
Again, all brands are not equal, and the brand can be more important than the mah rating.
I have energizer rechargeables, all purchased at the same time, at identical ratings and some have been duds others have been champs.