The developer stated that streaming was one of the biggest challenges on PS2, so imagine how bad it would have been on DC with only 1MB/s compared to PS2's 5.28MB/s.
Having 1/5 the streaming performance alone with half the system RAM of PS2 would have required substantial cut-backs to environment detail and complexity to keep the streaming requirements within the 1MB budget.
Streaming performance - in terms of sustained linear read - peaks at 1.8 MB/s on the outer edge of the disk on DC, so it's a little above 1/3 of the PS2's peak read rate.
Still a sizeable difference, but not bad from the DC.
The biggest challenge for streaming in a open world game isn't sustained linear read rate, but transfer rates when access times are accounted for. This is more complicated than just a single figure, where things like how fast the laser head can move (and perhaps re-focus), and even how fast the disk is physically rotating become important factors.
I've got some of the DC developer docs which have some info on the GD-Rom drive, but I've yet to find the equivalent for PS2, so I can't really compare them in this regard yet. I expect they'd be fairly similar, with maybe a negligibly lower rotational latency for the Dreamcast (~3000 rpm for DC vs ~2900 rpm for PS2) but a practical advantage for PS2 coming from data being more densely packed.
Edit: and with BluRay being so much higher capacity you could potentially duplicate key assets across the disk to reduce access times, but you'd need to carefully think out how you would do this.
PSP has 32MB (Latter models have 64MB) of system ram compared to DC's 16MB which is a huge advantage over DC.
PSP stored textures in main ram, so a fairer comparison would be 32MB vs 16MB + ~6MB, so 32MB vs about 22MB. Still an advantage for the PSP, but I think PSP used CLUT textures like PS2. In practice, this would have closed at least some of the 32MB vs ~22MB gap, potentially quite a bit.
PSP's UMD (1.37MB/s) also has a slightly higher transfer rate than DC's GD-ROM so sounds more of a game problem, than an issue with PSP's hardware and transfer rate.
Peak transfer rate of the GD-Rom was 1.8 MB/s, so a bit faster than PSP's UMD. Transfer rates for the GD-ROM were actually in the range between 900KB/s on the inner edge of the high density area (the part where games were stored) to 1.8MB/s on the outer. So an x2 difference between fastest and slowest - typically it's larger than this for an optical drive, but GD-Rom uses the slowest innermost section of the disk for none game purposes.
But I suspect a bigger problem for UMD than linear read rate are its reportedly awful access times. If you needed to read from somewhere else on the disk, it was slow to get there and start reading again and that represents dead time that slows down loading. The more often you have to move between different locations, the more you suffer. In the case of Crazy Taxi on PSP struggling when also streaming music off the UMD, I think there's a good chance that's primarily because of poor access times as the head moves repeatedly between game data and music data.
But I suppose that makes sense. The DC's GD-Rom drive was physically much bigger, could use vastly more power, could spin the disk much much faster (greatly lowering rotational latency), and almost certainly could move its read head across the surface of the disk faster.
For anyone that's interested, here is the GD-Rom outline page from Dreamcast developer docs: