The Neo Geo is still popular for all famous arcade games like King of Fighters. And people still play them for competition. You can't really say the same thing for the Super Famicom and the like.
Plus "power does not matter" does not make sense. It worked for Nintendo before. The SUper Famicom was the most powerful console at the time and it sold better than the Megadrive. The N64 did not beat the playstation but it was more powerful 3D-wise but they made the wrong choice to go with cartridges then. Nevertheless the N64 sold well and had very good games too.
The started dropping the ball with the Gamecube in terms of Raw Power - it was not better than the Xbox or the PS2 or at least not significantly to make any difference. And guess what, this is when Iwata was leading the design of the console. He is at the root of "we don't care about graphics, old-gen is the best". It did not work well. Even the Wii was not so much of a success- they sold a lot of hardware but very few games per system. Most consumers bought it for Wii Sports and left it at that and most units collected dust soon within a year of purchase.
The reason for Neo Geo being more popular than SNES in competitions is probably that the Neo Geo catalog was almost all competitive simultaneous 2-player games (as they doubled as arcade games), while in the SNES most iconic games are single-player. For SNES games with the simultaneous multiplayer mode (e.g. Super Mario Kart) championships are also healthy.
In my opinion SNES and Neo Geo were, each in its style, the best consoles of all time, and in general they have aged really well, as can also be seen by the persisting popularity of their games in 2017. I think this is probably because they were the pinnacle of 2D gaming. Of course 3D bought amazing possibilities to gaming, but for example the precious artfulness and attention to detail in Last Blade II (IMO a much better game than the overrated KoFs, by the way) is something I am still yet to see in a modern fighting game. On the other hand, when I play an early 3D game like many PSX releases, I just see things that can be done much better now, which makes the game look more dated.
The Neo-Geo is truly a way to bring games you would find in an arcade home while the SNES has long single player games which don't work in an arcade setting. So it's not that surprising the Neo-Geo games are more suitable for competition than most SNES games.
Xbox and PS2 were also sold at a loss for a long time, I don't think the xbox was breaking even on it's investment until late into the 360 lifetime. Nintendo can't compete on those terms, they aren't a wing of a huge multinational company (merely a small multi national company) that can take losses like that.
Plus "power does not matter" does not make sense. It worked for Nintendo before. The SUper Famicom was the most powerful console at the time and it sold better than the Megadrive. The N64 did not beat the playstation but it was more powerful 3D-wise but they made the wrong choice to go with cartridges then. Nevertheless the N64 sold well and had very good games too.
The started dropping the ball with the Gamecube in terms of Raw Power - it was not better than the Xbox or the PS2 or at least not significantly to make any difference. And guess what, this is when Iwata was leading the design of the console. He is at the root of "we don't care about graphics, old-gen is the best". It did not work well. Even the Wii was not so much of a success- they sold a lot of hardware but very few games per system. Most consumers bought it for Wii Sports and left it at that and most units collected dust soon within a year of purchase.