According to a list of Nintendo 3DS specs on Nintendo’s official website for the device, you can expect the 3DS’ battery to last you between 3 and 5 hours while playing 3DS software.
Playing regular Nintendo DS games on the 3DS won’t drain the battery as fast, and you can expect between 5 – 8 hours of battery life. Charging the battery completely could take up to 3.5 hours.
Nintendo’s spec sheet also reveals that you’ll be able to move digitally-purchased software (DSiWare) over from the DSi and DSiXL to your 3DS. However, there is an unspecified limit to the number of times you’ll be able to move a piece of software.