As I said, I went back to being a PC primary player which, for my tastes, was well beyond consoles at the time (and had online, etc). Never did get the Xbox OG.
But yeah, I'd still argue that PSO, sonic, soul caliber, etc in the ~2 years really shined over PS2 and remained the better versions (rez, thps, etc). Dreamcast was a true revolutionary step forward, and PS2 - which had wide range developer support - was just not as good. I can't speak in hypotheticals, but just overall preferred the hardware, games, and vision the DC represented over PS2.
Hope that doesn't "demolish" your sense of things too badly.
note that I was speaking of the Library of the PS2 compared to the DC and 360 specifically. "hardware and vision" of the DC doesn't amount to much if the games never showed up. Revolutionary steps forward are great and all, but for every positive the DC had it took several confusing steps back. Why did the controller have one analog stick long after two had been set as the standard by the PS1? Why was the DC using easily copied GD-Roms only barely larger than CDs when the industry had moved to DVD? The DC came with an internet adapter, but why was it a 56K modem if the system hit shelves in late 1999?
The DC in many, many ways as a hardware platform was a generational half step that "almost" did things right but couldn't quite get there. The OG Xbox on the other hand managed to get a lot of those things correct and was a more competent platform, even if its library is still not anywhere near as robust as the PS2's.
As for the Ps2 itself, that library has a sheer flood of extremely well regarded games exclusive to the PS2 that never showed up on the DC (or anywhere else, the PS2 has an absurd amount of exclusive titles), nor did anything like them. The only platform with an exclusive library as large as the PS2 is the NES, and that system had no real competition- the PS2 had plenty, but none of them managed to get any traction against it. It was simply too good at what the market wanted at that time, which was at that time local play, not online. The DC, GC, and OG Xbox all had robust online hardware available and software titles to match- all of them got crushed.
PSO, Sonic, and Soul Calibur are fine games, but in the first 12 months of the PS2's launch it already had Tekken Tag, FFX, Guitaroo man, Devil May Cry, Gran Turismo 3, Silent Hill 2, Ico, Red Faction, and Twisted Metal: Black. Go an additional 12 months to the PS2's second year and you add Frequency, Burnout 1 and 2, Crash: Wrath of Cortex, Fatal Frame, Dynasty Tactics, Kingdom Hearts, GTA: Vice City and Breath of Fire: Dragon Quarter.
The DC's library in its lifespan doesn't stack up to this, and this is only through 2002. The PS2 continued to receive genre setting games on the system for another ten years- Guitar Hero for instance was a breakout PS2 title that spawned an entire mainstream genre. No such title exists on the DC- nor could it have. The lack of storage space on the GD rom would have prevented it. The DC had a handful of quality games that had potential, but the system itself never realized it, and lack of foresight in the design meant it never would have.