Actually, I have a reasoning to make my way around that as well - Summons don't stay the same from aeon to aeon, world to world. They can get old and when they do, some new soul comes along - often human - and takes over the role. So the Bahamut of FFIV got tired and Kain took over the role.

I was thinking over something and I actually think now that he wasn't the weakest of the three materia, but probably Neo Bahamut - with the Bahamut that was before him being Bahamut ZERO and plain Bahamut being FFX Bahamut instead. I don't know however what happened to him, he might have been the unfortunate who became Tiamat (a very big point in Griever's life, as he gave himself over to Ultimecia to protect the rest of the GFs from suffering the same fate as Tiamat).