If they're moderated batteries, it sounds like the moderation (voltage adjustment to be consistent) has gone awry. When it's about halfway done, the vape shouldn't be so burned. When the battery is nearly empty, the vape should be thin and cool if that's the case.
If the battery isn't moderated, then that's just strange...
Since the same cartomizer gives you a good vape on one battery but not on another, try another cartomizer. It could be that the air flow through that particular cartomizer is just a little tight on that particular battery. If that solves it, don't use that particular cart on that particular battery.
If several different cartomizers act the same, I'd say the battery has something wrong with it.