Legend of Zelda: Four Swords not showing up on Nintendo eShop

Because the 3DS lacks any sort of capability to use the Game Link cable, the only way you could connect your old games to the new 3DS ones is by using the password system. The 3DS version seems to accept passwords and secrets the same way the original games did, so you should be able to input them with no problem, as the games are direct ports from the old cartridge versions, with no changes. (they even still mention using the Game Link cable!)

Cons of Downloaded Games:

• Can't share with friends
• Difficult to move from system to system
• Leaves cartridge slot empty (no placeholder)

Cons of Physical Cartridges:

• You are unable to back-up data into an SD card
• Need to carry/swap cartridges
• No possibility of recovery*

^{* Never assume Nintendo will get your digitally downloaded games back either. That being said, anecdotal evidence:}
I recently purchased a 3DS and purchased and downloaded a game. A week in, my hinges began loosening, so rather than sending it in for repair, I wanted to replace it at the retailer. I called Nintendo support, who told me that if I made sure to register my current 3DS first, and write down my serial number, they would be able to initiate a system transfer remotely, after I had exchanged my system. They said this is a new option, and I think it seems to be a step in the right direction. I swapped my system, and called them back. Unfortunately, their phones have been too busy to even put me in a queue for the last several evenings, so I can't yet confirm that this will in fact work, and am now left with a 3DS and none of my downloaded games. For now, this is definitely another pro for cartridges.

Really, it comes down to security of a physical copy vs convenience of a digital one. Personally it's physical cartridges for me from here on out, until Nintendo moves to a real account-based system.