since the two cultures were in contact for centuries, why didn’t they both adopt one of these forms of writing material as superior one? E.g. why didn’t people in Mesopotamia (which had plenty of marshes of their own, just like Nile delta) start growing papyrus? Elsewhere e.g. the Greeks were quite happy to adopt the papyrus even when that required importing it from Egypt.
The Egyptian did adopt clay tablets (or invented them independently). The Tel El Amarna Latters, for one collection, are all on clay tablets:
One WAG: The writing systems were largely driven by the writing materials themselves. My guess is the writing of hieroglyphs–even the demotic forms–was too difficult on clay (the Amarna letters mentioned by CalMeacham are in Akkadian, and IIRC mostly deal with foreign affairs, i.e. they weren’t intra-egyptian communications).
For the reverse direction, cuneiform on papyrus would certainly not be difficult–and cuneiform was certainly used on monuments like hieroglyphs in Egypt. Perhaps the Akkadians/Assyrians saw no advantage in papyrus given their less-decorative writing system (i.e. I would guess the time required to write cuneiform on clay vs. papyrus was roughly the same).
Clay tablets, unlike papyrus, do not rot and do not burn, arguably making them more durable. Combine that with a system of writing suited to using a stylus and soft clay and cuneiform users had little incentive to switch to papyrus.
Meanwhile, the Egyptian writing system was so ill suited to soft clay that as long as papyrus was cheap and plentiful there was little incentive to switch.
No doubt there was some cross-over, and both groups carved their writing on walls, but one tends to use the writing materials one is used to and which are suitable for one’s language.