OK, this happens a lot. It's happened to me, and to hubby, and to a couple of members here at least. Here's what you need to do:
So long as you transferred EVERYTHING from the old card to the new one, it's all still there. Put your new card into the SD slot of your computer and open it up. Make a back up onto your computer, and to be extra safe onto a thumb drive as well. There will be two folders on the card, DCIM (where all your photos etc are stored) and Nintendo 3DS (where all your game data and downloaded games etc are stored). Open up Nintendo 3DS. In here there are two (or more) folders, one is a string of alpha-numeric gibberish and the other is called Private. If you have two folders with alpha-numeric gibberish names, you need to merge the largest one (the one holding the most data) into the latest one (the one with the latest/most recent date/time). You can skip any files that have the same name.
I had to do this fairly recently for hubby, who got a new (bigger) SD card for his 3DS. I transferred everything from the old one to the new one using the computer, but it looked as though all his downloaded game saves were gone. Nearly a year's worth of Layton, Mario Kart etc, all gone. Except they weren't. What happened was that, instead of accessing the data I'd so painstakingly transferred over, the 3DS created a new folder and accessed that instead. It was as though all that data had just disappeared. When I redownloaded all the games that were no longer there (but the E-Shop still knew he'd paid for them) I realised something was odd about the number of blocks remaining on the card. I'd doubled the size of the card, but after re-downloading all his existing games there was still not much space left. Conclusion - the card had the same data on it twice.
ETA - once you've verified that everything works as it should, you can remove that extra folder. It's only taking up blocks on your card. Back it all up again first though, in case you delete the wrong folder.
Edited again to add - when you do the folder merge, you need to make sure you are merging INTO the folder with the most recent date, as this is the folder your 3DS now looks in for data. The other folder is the one it used to use, before you changed cards. Also, if you have been playing much since you made the initial change-over and you skip all the same-name files in the merge you may lose your most recent save data. I checked each file date before deciding whether to skip it or keep it.
Edit - the above was taken from a post to a member who had changed their SD card for a bigger one. You are using the same SD card in a new system. The procedure is the same, put your SD card in your computer, back it up, merge those folders, put the card back in the 3DS to make sure everything's as it should be.
