In my experience the Activity Log is inaccurate for DS and DSi titles when you've suspended them across midnight.
When I first got my 3DS, I noticed it discarding any played time before midnight if I suspended it overnight - I'd play a game for an hour before bed, go to sleep, play an hour the next day, then quit and check the Activity Log, and I'd see a single hour played.
Recently, this hasn't happened, but instead I seem to have the entire day counted as one play session even if I took suspend breaks during the course of the day. I cannot say if this changed one of the firmware updates, or if it's just another symptom of the same underlying bug.
I only recall one game that counted suspend time against the in-game timer, Hotel Dusk, in which I racked up about 150 hours of supposed play time. If Activity Log is accurate, it should always be longer than the in-game reported time. It will count time in save menus, option screens, music players, replays if you give up and come back later at an earlier save point, and so on.
Which is more accurate depends on the kind of game, but in general the in-game time is probably more accurate, especially if you are trying to gauge the length of a game.
I just did a system transfer from my 2 year old 3DS to a new 3DS XL. With the current version of the 3DS software, after the transfer is done, the new 3DS wants to use the old 3DS's SD Card. So going through the standard System Transfer process would do exactly what you want!
In my case, I wanted to use the new 3DS XL's SD card since it was bigger than the old 3DS's one. Nintendo has a pretty easy process for this: http://en-americas-support.nintendo.com/app/answers/detail/a_id/309. It's essentially copying the contents of the SD card from old one to the new one via your computer's SD card reader.
Best Answer
The 3DS does have internal storage.
It is also used for storing downloadable games originally made for the DSi:
(emphasis added)
These DSiWare titles can be stored on the SD card, but they can't be run unless they're on the internal memory (the System Settings will allow you to move them). From the original 3DS operations manual (English, p. 72):