i dont understand 100% of what you are talking about, but +1.

all the smart people called the first two playstations the Piece of Shit and the Piece of Shit 2 because that is all they were compared to what Sega made.
Uh.. PS2 is more powerful than Dreamcast in just about every other area. Faster CPUs, more GFLOPS, double the main RAM, far higher polygon rate, etc.
The only thing it really lacked in compared to Dreamcast was VRAM.
I seem to have my Dreamcast info wrong anyway. Appears it was a single SH4 (I thought it was 2 x SH4 SMP) and only 8 MB VRAM (I thought 16MB).
My time with DC was very very brief and it was a long time ago. I learned just enough to get to know the architecture of the PVR tile rendering and some of the SH4s 128 bit vector ops.
But the specs are of the top of my head:
PS2:
MIPS R5900
~300 MHz
6.2 GFLOPs
32 MB RDRAM @ 3.2 GB/s
4 MB VRAM embedded RDRAM on die in "GS"
~20-75 million polys per sec ?
DVD-ROM 8.5 GB capacity
-128 bit main bus throughout (64 bit QWORD and 128 bit DQWORD if I recall the terminology)
-Smart autonomous chainable packet driven DMA controller
-TWO completely stand alone 128 bit dedicated dual integer/vector pipe SIMD processors with their own instruction sets and RAM (VU0 and VU1)
-128 bit registers in the R5900 "EE"
-dedicated VIF/GIF/SIF/etc interfaces that could automatically arbitrate contentions between DMA and the target devices (eg: insert stalls), and automatically pack and unpack RGBA/XYZW data to and from a number of formats in flight
-sound processor was actually an entire 33 MHz MIPS R3300 with everything needed to natively run PS1 games for BC but could be a coprocessor and run .irx modules to offload all I/O devices in PS2 mode.
-Graphics Synthesizer: 48 GB/s to it's 4MB embedded RDRAM, 16 pixel raster pipe, 2560 bit internal bus, 2.4 giga pixels per second (1.2 textured).
-VU1 closely coupled to GS acting as the geometry processor for all lighting, transform, clipping, geometry CREATION (aka subdivision surfaces), etc. VU1 was effectively a completely programmable vertex shader that ran it's own programs completely independent of the main CPU.
-no antialiasing but the CRTC could be programmed with two frame buffer addresses (in practice, just slightly shifted addresses of the same framebuffer) and alpha blend them to both hide the low texture color depths and provide fake pseudo antialiasing, motion blur, depth of field, etc type effects.
DC:
Hitachi SH4
200 MHz
1.4 GFLOPs
16 MB SDRAM @ 1.5 GB/s
8 MB VRAM
~ 3-6 million polys per sec
GD-ROM 1.x GB capacity
-128 bit SIMD vector and matrix instructions built into the SH4
-PVR @ 3.2 gigapixels/s untextured?
-hardware texture compression
-not much custom or special about Dreamcast architecture. Standard CPU connected to some RAM and a PC PVR2 rasterizer connected to some VRAM. Very easy to program. All geometry, transform, lighting, matrix, vertex, clipping etc operations carried out on the main CPU in software. PVR simply accepts finished 2D triangle display lists, sorts the triangles into pixels/spanlines into tile bins, then renders the pixels to the framebuffer with 0 overdraw.
-hardware anti aliasing built into PVR2? trivial and natural due to it's deferred rendering approach and knowing all triangles and pixels in the scene before any writes to the framebuffer occur. All rendering gets sent through a "cheese grater" where everything gets sent not to the frame buffer, but subdivided and dumped into tile bins/display lists for individual parts of the screen, which are then processed LATER in an on die tile buffer and blasted to the frame buffer tile by tile (IIRC).
From what I can remember and sort through on the web, DC had more video ram, even more with texture compression, and more fill rate, and anti aliasing. Explains why DC games are more vibrant and colorful than most PS2 games that look dull and washed out by comparison. PS2 struggled with maximum texture size and used 8 bit CLUT and 15/16 bit texture formats more often than 24/32 bit textures. While Dreamcast was likely able to losslessly compress 8:8:8:8 or 5:6:5:0 RGBA textures into it's 8 MB VRAM, PS2 was more likely to be using 8 bit CLUT textures as it's "compression" in it's 4 MB VRAM.
But PS2 pretty much DWARFED the Dreamcast in everything else; it certainly wasn't a piece of shit. To be fair I don't have as much detail on Dreamcast because I had far more programming time on PS2 simply because it was more complicated to program and that equates to more fun for me. I like playing with oddball multi processor architectures that look completely unlike anything else I've ever programmed.
So DC looked prettier, but what you saw up front is what you got, there wouldn't have been much room for improvement. It probably would have always looked better than PS2. As later PS2 games got more complex and started implementing multiple render passes, render to texture, etc, the low color depth, relatively plain blurry textures, and lack of precision and dithering from being crammed from lack of VRAM became even more apparent.
PS2 didn't look as pretty but was capable of creating far more immersive game environments (more objects, more complex geometry and particle systems, more complex physics effects, deeper AI, etc). When programmers were able to program the system properly asynchronously with minimal stalling and maximum concurrency and utilizing ALL processing units including the often overlooked VU0, it would dwarf the Dreamcast in raw power.