I'll break it down for ya, since the above guy didn't do a good job of explaining everything.
3DS it doesn't run at all, it just uses an outdated version of Gateway which is essentially a custom firmware obfuscated with hardware and if you try to use a new version of Gateway, it will probably brick your console deliberately. The gateway team is brick happy with clone carts. Gateway itself requires firmware of 9.2 or below [10.3 if you are willing to attempt a downgrade, but at that point, it's easier to use CFW, which I'll talk about in a bit.]
Everything else on the DSTwo+ runs in the DS mode of the cart and is thus restricted to the power of the DS Lite, and the DSTwo's Internal Processor. Only GBA and SNES use the Internal Processor of the DSTwo, keep that in mind.
DS it runs perfectly save for a few Super Mario 64 DS romhacks. This is the main draw of the DSTwo, as it has an In-Game Menu activated by a customizable button combination, where you can save/load savestates, view guide images and texts saved on the SD card, turn AR Codes on and off, and even search for new codes. The DSTwo does NOT support DSiware or DSi-Only games. DS is the only thing that you can't do better on a 3DS with CFW installed. CFW does NOT support DS games in any way, shape, or form. The interface for DS games in DSTwo is really nice, and you can even theme it if you have the desire to do that.
GBA via TempGBA runs alright, but it's far from hardware accurate like a DSlite with a Slot2 cart. Emulation is kind of stilted, there's many games that won't work or just don't run well. Look on WikiTemp for a compatibility list. [The preferred method is to use a 3DS CFW to run either Retroarch or mGBA on n3DS, if you're into hardware accurate stuff, you can convert GBA roms to GBA Virtual Console cias to install in CFW, but that can get a bit annoying to work with because they need to be installed on both SysNAND and EmuNAND.]
GB and GBC you run under GameYob which is essentially perfect. [You can also run GameYob in 3DS mode with a CFW or Homebrew Launcher]
Genesis you use jEnesisDS with, and while the emulation is good, the screen isn't high enough resolution to display full genesis games on screen so you have to use screen scrolling techniques. [3DS with CFW can run Genesis injects into the 3D Sonic 2 game, but that is buggy and kind of a crap option as well. Retroarch works well enough on the n3DS but slow and crap on the o3DS. No screen size issues in 3DS mode]
NES under NesDS is actually super perfect but uses scroll techniques and interfacing to make the game fit the screen. [3DS with CFW doesn't have this issue obviously because the screen has more pixels in 3DS mode then in DS mode.]
SNES via CATSFC is also just alright, like the GBA, but it doesn't run well, doesn't support all SNES games, and it's not super accurate emulation. [Running a 3DS with CFW or homebrew launcher and blargSNES is a much better option, although support for games isn't as good, the emulation is much faster when it works which means its both more playable and it doesn't have screen size issues.)
Bonus!: Game Gear and SMS via S8. Also perfect, very good emulation.
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Overall, the DSTwo is still the best flashcart around, albeit a bit pricey.
I'm able to run my DSTwo even via my CFW in EmuNAND on my 3DS, and I do not use it's Gateway feature, since it is rather buggy.
I would recommend you use a DSTwo in Addition to having a fully fledged CFW on your 3DS side, such as rxTools, and using the DSTwo+ as an original DSTwo.
CFW is a fairly complicated setup on all 3DS systems, the n3DS personally, I've never set CFW up for, but I hear it's not that much harder.
One thing to keep in mind about the DSTwo is that it's processor can drain your battery, even if it's not in use because it draws power from the 3DS any time it is plugged in, personally, I just keep the DSTwo in the 3DS but not totally inserted until I want to use it, to circumvent this issue.
That's about all I think you should need to know.