If you buy a physical copy on the 3DS, does it need to download

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.

You can link a single ID to your 3DS and Wii U (this is a fairly recent change). But the games are not "cross buy" in any way similar to the Playstation ecosystem. You can upgrade Wii VC games to Wii U (only if they physically reside on the Wii U console), but buying [GAME] on Wii U, much less Wii, doesn't entitle you to [GAME] on 3DS even if [GAME] is on both. There's also no way to move save data between either system, with case-by-case exceptions (you can do this in Monster Hunter 3 U, but only because of a companion app, it's not built-in functionality like it is on Playstation 3/4/V)

The consoles are joined by ID, but really only for Miiverse, Club Nintendo and eShop balance purposes. This has been a common complaint about Nintendo's ecosystem but there have been no announced plans to change this on the current consoles.