On your command.
I'd say it's a tie. The DS is better than the PS1 in a lot of areas, the PS1 advantages all contributing to making the top PS1 games look better (in overall) than DS games.
- Renders at 18-bit color: providing a clean image free of
dithering;
-
Perspective correct texture mapping avoids the "zig-zag" or "wavy" textures seen on PS1 games;
- Polygons shake/snap a lot less in DS games due to higher precision geometry transformations (32-bits versus 12-bits);
- True skeletal animation due to much faster CPU and hardware-accelerated transform & lighting;
- Hardware-accelerated polygon clipping and backface culling.
- Hardware support for cel-shading, outlines, stencil-buffer and reflection mapping;
- Free edge antialiasing.
But the PS1 had some advantages:
- 600~700MB discs (being able to use multiple discs if needed), while most DS games are smaller than 256MBs.
- Supports additive and substractive blending modes, while the DS only supports alpha-blending (like the N64 did);
- Higher polygon throughput (180K tris/s versus 120K tris/s on the DS);
- More flexible rendering pipeline (but harder to program for);
- The top-games had much bigger budgets than DS games;
The DS has a very strange way of dealing with polygons, in that it always runs at 60fps and draws 2048 polygons per frame. Only polygons which are visible on the screen count for that number (after clipping/culling) and anything over that is simply skipped. If you want your game to run at 30fps and get twice the polygons you need to jump through hoops and draw the scene in two passes, sacrificing some VRAM and dropping from 18bpp to 16bpp to do so.
The PS1 would just reduce the framerate if you pushed more than 3000 triangles per frame. So a 20fps game could push 9K triangles per frame (FFIX battles).
The budget/development philosophy was very different: the top PS1 games were bona-fied blockbusters where developers were constantly attempting to out-do each other in technical prowess while even the top DS games are developed with a safer and more budget-conscious approach.
Crash Bandicoot is a great example: there's nothing on the DS like it (but the Wizard of Oz game gets very close - and runs at 60fps). But if you read the
article about it, there's nothing preventing a DS game from using the same streaming technique. But it's such a ludicrous and laborious technique that no DS dev would get a budget approved for that.