are the XBP09-DPUIT-156 and the XBP9B-DMWT-002 modules compatible with each other?

Can these two modules take to one another?

No, they are not compatible with each other i.e. it is not possible to setup a communication link between them.

Although, if you are planning to replace all XBP09-DPUIT-156 in your setup with XBP9B-DMWT-002, then it shouldn’t be much of an issue. They share common pins layout design.