Some of my best gaming memories are from "duet" campaigns. I've run them using a bunch of different systems. While I do think that some systems might be a bit better suited to duet games, I don't think the system matters as much as the mindset the game is approached with. If the participants (GM especially) goes in with a classic view that you require X number of PCs to be able to meet the "default challenge level" of the game, then there will be issues. As long as the GM is willing to accept that a single PC is limited to what kinds of challenges they can overcome, and is willing to present a world that has those kinds of challenges in it, the game will work great! I have never understood why many GMs insist that singular PCs must be accompanied by a number of GMPCs so the proper "balance" can be achieved. The GM has the power to simply present situations that a PC can deal with without having to have GMPCs accompany them. It's really not that hard, you just need a GM with a halfway decent imagination.
For me the biggest change, as others have alluded to above, is time scale. In a duet game the time scale can fluctuate enormously compared to a group game. There is only a single player who's perspective matters, and who is responsible for all of the player narrative. Things can happen way faster than in a group game as only the events involving a single PC need to be dealt with. They can also happen a lot slower as the single player may decide to focus on an aspect of the narrative that would be ignored in a group game simply because not all the other players are on board with said aspect. I've also found that duet games feature far more frequent "time jumps" as it's all up to one player whether or not weeks or months of time gets skipped.
The one key thing I try to include in any duet game is a "home base" of some kind. It can be a traditional base, like a village, or castle, or space station. Or it can be a mobile base that has a crew of some kind if the game is going to feature travel as a key aspect. The reason for this is to have a cast of NPCs available for the PC to interact with. Which is what I consider to be the most important thing in a good duet game. The GM really needs to work extra hard to make the world feel alive as there are no other players for the lone player to interact with. All social interaction will be with NPCs through interaction with the GM. While I don't necessarily start the PC off with a base, it is something I will attempt to work into the game as soon as it makes sense. I also try to introduce a fair number of potentially recurring NPCs fairly early in the narrative as a way to help tie the PC to the world. Even better if the player creates the PC with already existing ties as it just makes my job as GM that much easier.
I have found, that while I do believe that you can run a duet game with any system in any genre, some are more suited for it than others. As mentioned above, Burning Wheel is perfectly suited for a duet experience as the entirety of the system is hyper focused on the narrative revolving around the PC and their personal goals and personality quirks. I also had a phenomenal experience running a duet Vampire game that, for once, didn't devolve into a trench coat and katanas game as I was able to keep it very focused on the PC's personal horror as they dealt with the reality of becoming a Vampire. Generally the less focused a game is on combat, and the more robust it's mechanical and genre support for non-combat activities, the more likely one is to have a successful campaign. I mean, I guess one could run a combat heavy duet game where the PC is accompanied by several GMPCs, but why bother...just play a minis combat game instead.
My 2 cents anyway. Cheers!