No it doesn't. People need to stop believing this.

AMD for example has consistently iterated upon it's Graphics Core Next design...
A 4 Teraflop Graphics Core Next 1.0 GPU will loose to a 4 Teraflop Graphics Core Next 5.0 GPU. - I can even demonstrate this if you want.

Here we have the Radeon 7970 (4.0 - 4.3 Teraflop) against the Radeon 280 (2.96 - 3.34 Teraflop).
The Radeon 7970 should be able to wipe the floor with it's almost 1 Teraflop advantage right? Wrong.
https://www.anandtech.com/bench/product/1722?vs=1751

They are both Graphics Core Next.
Again, Flops is irrelevant.

FLOPS is a Theoretical number, not a real world one. The GPU in the Playstation 4 Pro and Xbox One X can do more work per flop than the base Xbox One and Playstation 4 consoles, that's a fact, due to efficiency tweaks in other areas.

Ports over from the PC to the Xbox did shine on the Xbox though.

Nah. - You are very wrong.
For one, Gekko is a 32bit not a 128bit processor.
https://en.wikipedia.org/wiki/Gekko_(microprocessor)

Bits do not correspond to performance either... Most games wouldn't have leveraged the 64bit registers anyway either as it would consume more Ram.
Bits are not a representation of performance.

The Celeron 733mhz, Again beats the 500Mhz PowerPC equivalent of the Gamecubes CPU... That ignores the fact the Gamecubes CPU is clocked lower and the Xbox's CPU has performance enhancements over that.
The P6 derived core of Intels chips typically always had a pretty decent industry leading edge for the most part.

Even Anandtech recognizes the Intel chip would be superior. https://www.anandtech.com/show/858/2

There are many aspects where the Gamecubes GPU is better than the Xbox's GPU.
But there are many aspects where the Xbox's GPU is better than the Gamecubes.

However... The strengths of the Xbox GPU tended to outweigh it's limitations, hence why it's games were typically a step up overall.

More false information.
The Xbox CPU is not x64, 64bit extensions weren't tacked on until Intel adopted AMD x86-x64 extensions (AKA. EM64T) with the Prescott variant of the Pentium 4.
https://en.wikipedia.org/wiki/X86-64
https://en.wikipedia.org/wiki/Pentium_4#Prescott

The Xbox CPU is x86 as it's Pentium 3 derived.
https://en.wikipedia.org/wiki/Pentium_III
https://en.wikipedia.org/wiki/Xbox_technical_specifications

Because Rogue Leader leveraged the Gamecubes GPU strengths rather than the Xbox's.
If you were to make a shader heavy game that gobbled up Ram like no tomorrow... The Gamecube would also struggle.

They could be including Vertex performance in that calculation.
Citing nVidia is a pretty dubious affair, because nVidia will want to fluff up numbers as much as possible.

To correct earlier assumptions, the "Gekko" CPU that powers the Gamecube is 32-Bit.  The "Flipper" GPU is 64-Bit.

Yeah - I remember around that time people were using some wild numbers, 400 or so GFLOPS. Which when you get down to math, it really comes to something as silly as that:

(24x27FLOPS + 8x10FLOPS)*550MHz = 400GFLOPS

And those 27 per cycle and 10 per cycle numbers are indeed from official nVidia document - or it seems so...   https://www.pcper.com/reviews/Graphics-Cards/NVIDIA-GeForce-7800-GTX-GPU-Review/Hardware-Details

Yet again, 192GFLOPS for whole GPU is from official nVidia document as well...  https://www.nvidia.com/content/PDF/tegra_white_papers/Tegra_K1_whitepaper_v1.0.pdf#page=18

This is the very reason why i said I would love to see math behind those numbes for GC and XBOX - because, without knowing underlying architectures it's just guesswork, and given base config (4:1:4:4@162MHz  vs 4:2:8:4@233MHz), some of those numbers look...well, quite silly.

I thought the base PS4 and Xbox One GPUs were only one GCN generation behind those of the Pro and One X, but on further investigation, turns out it's actually two. So yeah, the performance difference is probably a fair bit more than the raw FLOPS value alone would indicate (and that's before you take into account that the One X's new memory set-up completely blows the doors off those of the older models).

Was the GC documentation even available in english then ? IIRC Nintendo was extremely late to the party when it came to international documentation for devs, which would have made it much easier for western devs to get the full power of the OG Xbox compared to the GC.

Edit : tried to check it out it seems false. My terrible memory at it again, sorry.

Well that's just the thing, it seems what ever game focused on said console will outperform the other. However I strongly disagree when people claim the Xbox to be the most powerful console of the 6th gen. In my opinion it was the GC. I believe the GC could run any Xbox game where as I see the Xbox struggling to run games built around the GC's hardware. As examples, Splinter Cell was designed around the Xbox hardware and the GC could run it (Not as good) but far from broken, where as the Xbox judging by Rogue Leader could barely do half the frame rate of the GC version, hence why there was no Xbox port. Now that's just rumours stated from Factor 5 at the time.

Xbox also had better multiplats because its design was very similar to PCs where as the GC like most consoles were alienated and were a little harder to work with, so in many cases the lead platform was Xbox.

I also strongly disagree when people say the Xbox could render the better looking water.. I find it that gen that the best looking water in games were on the GC. Games like Mario Sunshine looked absolutely amazing and the GC was actually rendering the waves, it wasn't just a texture placed ontop of another texture to make the water detail look good and mimic waves, it actually did waves. Also Wave Race Blue Storm still has some of the best wave effects iv seen apart from Black Flag and Sea of Thieves and that game was made 17 years ago.

https://www.youtube.com/watch?v=4q7qMwe3_zk

I just find the Xbox's design just wasn't as good as the GCs. I find the Xbox had bigger bottle necks when it came to things where as the GC had a perfect blend between CPU and GPU. Xbox was all about brute force and basically was a supercharged PS2 however the GC was a cleverly designed machine capable of much more with less horse power.

Also keep in mind that Nintendo was very honest with there numbers of the GC, claiming low poly figures but with using a bunch of effects where as PS2 and Xbox claimed they could do more polygons but without any effects, basically wireframe mode. 

Doom 3, Chronicles of Riddick, Morrowind...to name a few...I doubt they could've run on GC without some serious cutbacks.

Yes, GC was polygon pusher, but XBOX had more capable and modern GPU.

I'm no tech guy but I had a GameCube and a PS2 that generation. The GameCube definitely had some great looking software but I don't think it ever had the best version of any multi-platform games aside from a few occasions (ie: RE4 after it got ported to PS2). There were a few times where the GameCube port was so bad, it was embarrassing. For example, I bought True Crime for the "Cube. It ran okay but I noticed that there was music listed in the manual that I never heard. I swapped it for the PS2 version. There was more music, more missions, better performance, etc. I was actually mad at how poorly the GameCube was being treated. Other examples included SSX, Splinter Cell (whole levels had to be redesigned for the Cube and PS2).

That could come down to storage media and how much effort went into a port, though.

Another example of how mulriplats can't really be the deciding factor: I remember reading that the Xbox version of MGS2 was way less capable than the PS2 version.

To summon up, Xbox was much stronger than GC and PS2 with a wide margin.