Hi Alex, sadly the only way to play homebrew games on your New 3DS is to get Cubic Ninja and install Ninjhax or get Ocarina of Time with a Powersaves pro to install OOTHAX in order to run homebrew.
There is a GBA emulator named mGBA that runs pretty good with the New 3DS in 10.3 (Not full speed so far but they'll get there).
And you can use Blargsnes 1.3 to play the SNES Zelda games.
If you want to play 3DS roms the only option for 10.3 is Sky3ds, they are releasing a new one called Sky3ds+ so you can check information about it.
You could even load a Cubic Ninja rom in the Sky3ds+ and load homebrew from there.
I've been doing some research on the Internet in regards to playing emulators on a 3DS running the latest firmware and there are posts and videos on YouTube of people claiming that the Supercard DSTWO Plus is capable of emulating on the latest 3DS Firmware but not 3DS titles just everything DS and earlier.
Can someone confirm this? Because I wouldn't mind purchasing a Supercard DSTWO Plus if that is the case.
Also, I have a copy of LOZOOT the actual game card. Can you show me what else I need to do at this point?
What is currently running emulators better at the moment Homebrew or Flashcarts?