I very much doubt that. nintendo consoles are usually slightly underpowered compared to their competitors. nintendo relies more on "gimmick" and their family friendly appeal.
Yep, the GC was more powerful than the PS2. Not sure how it compares to the XBOX.
Nintendo had pretty good hardware both with the SNES and the GC.
The fact that the GC was beaten by the PS2 was a concurrence of factors:
1) The PlayStation brand had MUCH more mindshare than Nintendo's back then. Whenever people thought "videogames" they thought of "playstation". The PS1 was a smashing hit and it blew the N64 out the water. The PS2 costed more than the GC, but everyone wanted a PS2 since the PS1 was so freaking awesome and the PS2 was one number bigger so automatically better.
2) The GC didn't have as much third party support as the PS2 did as Nintendo lost most of it with the N64. Most of them didn't want to develop for the weird-ass N64 hardware (seriously it was a nightmare to program it for) nor did want to pay the huge royalties and production costs for a cartridge-based system back when optical supports were all the rage. When the GC came out, they were still burned by Nintendo's last console and didn't risk much in the new one.
3) The PS2 was also a DVD player, the GC was not. It was a big thing for many people back then to get a game console AND a DVD player in the same package for the price of a standalone DVD player (those things were expensive back then!). Sony repeated this with the PS3 and it was pretty much the only thing which moved PS3s for the first 3-4 years, since it didn't have any GAEMS.
So yeah, Nintendo did it totally wrong with the N64 and they paid for it with the GC.
The GC's failure also lead to the "gimmicky" Nintendo which we're seeing nowadays. Since the GC was more powerful than the rest, but it didn't make any difference to sales, they just thought that it wasn't worth spending money and time in having the most powerful platform around.
The Wii, DS and 3DS proved them "right". People bought the Wii because of the gimmick craze, the DS had an epic headstart on the PSP thanks to the success of the GBA which made Nintendo the point of reference for people when it came for handhelds. The PSP never recovered and as such the 3DS surfed on the DS' success - PS Vita was destroyed thanks to the fact that when people think "portable console" they now think either DS or 3DS.
The WiiU tanked because, well: at first everyone thought that it was the same thing as the Wii. Then as soon as people started realising that the WiiU was a different console, third parties quickly abandoned it because ports were expensive (different architecture, less powerful than the rest meant downgraded ports, etc) and the few games that were released didn't sell well (as opposed to the Wii, where every shit game would sell at least a few hundred thousand copies) and we know the rest.