This is gonna be the thread where we talk about stuff

Loss of battery life is likely something you'll only end up noticing after several years, since it's the result of wear and tear on the battery's internal components due to electricity running through them. If the battery is on, this wear and tear is going to occur anyway, although there might be a slight difference depending on if it's plugged in or not.

So if you tend to turn your DS off, rather than putting it into sleep mode, then "topping it off" is more efficient. If you keep it on most of the time, it probably won't matter.

Either way, you're probably not going to notice much of a difference for several years. I've had my DS for...somewhere around 2-3 years, and the battery life has dropped by maybe half an hour, even with me leaving it plugged in overnight almost constantly.