There seems to be a lot of misunderstanding on what these chips do. I'll explain.
The DSP-1, I believe, deals entirely with creating pseudo 3D effects through the use of mode 7 and HDMA, as seen in Mario Kart and F-Zero (F-Zero does not use DSP-1, if I remember, but it's the same idea). The ROM for the DSP-1 is built into the chip, and therefore cannot be changed.
The Cx4 is a generic, I believe 20mhz ARM processor (similar in speeds to the SuperFX, but a different architecture) that gets its ROM from the cartridge. It is similar to the SuperFX and SA-1 in some ways, but it has it's own dedicated memory, it cannot access the SNES memory, nor can it access the ROM (Without some clever doing). If you do not need it's functions and you aren't writing your own code with it, it will do nothing for you. It cannot run 65c816 assembly, so it will never be able to speed up SMW without a significant rewrite that is super not worth it.
Originally posted by Mariofan64The effect on the amount of slowdown the game deals with.
None, unless you were previously attempting to do rotation, scaling, cot, etc. on the 65c816, then a bunch.
Originally posted by Mariofan64Extra upgrade effects each of them brings to the game
He linked this in the ASM.
Originally posted by Mariofan64I know that SA-1 and Super FX expand the amount of sprite on screen and per level
No they do not. There were patches made around the SA-1 that allow for a greater number of sprites on screen, but SA-1 is just a faster version of the 65c816 (more or less). You could make a patch that allows for an increase of the number of sprites on screen without SA-1.
Originally posted by Mariofan64The degree of incompatibility each would have with other tools and patches.
Shouldn't have any incompatibilities at all, since it's a co processor in the purest sense of the word. It's all about how you use it.
Originally posted by Mariofan64Based on what I have heard thus far, DSP-1 definitely seems to be the superior chip compared to CX4.
No, because it's not programmable and really can't do that much.
These really are developer tools, and that's great, but the normal user would not have much use for them. But it's still super great.