Considering that the DS carts don't use batteries to keep track of time or save data, I think they would be safer.
Also, I have not had a battery on a GBA cart die lose any game data. Only the clock events are affected, and that isn't a big deal, as being able to get access to a mediocre Leftovers wannabe and some berries which won't affect the story or team building in any real way won't ruin it.
GBA carts don't use volatile memory like the GameBoy Color Pokémon games. Those used a battery not just for the clock and weekly calender, but also for storing the save data. GBA carts don't do that, they use a more stable form of ROM. It was also more expensive, which is why bootleg GBA carts tended to use cheaper battery-powered ROMs that tended to die most of the time.
The choice is yours. Eventually, any storage medium is going to fail, but it looks like the GBA carts are good for at least a few more years.
Besides... if all goes well over the next few years, we may be seeing either more GBA games (including some pokémon ones) or 3rd gen remakes on the 3DS. If we get remakes, you might just be able to transfer all your favorites over and have them live in a reverberated Hoenn.