A battery that has more capacity is fine, as long as you keep an eye on how much space you have for the battery. If you have a 3000mAh battery, and you want to put a 10,000 mAh in it, then you may have an issue, but if you want to put a 4,000mAh battery in it, and its roughly the same size, GO FOR IT.
Original batteries or aftermarket really doesn't matter much. What DOES matter is the manufacture. Some are crap, some are gold. Don't cheap out on power, whether batteries or power supplies.