What do you mean by "compatible"? IBM software historically has been upward compatible -- my site has programs running in production that were last compiled in the 80's or even 70's, yet they keep on running fine despite many, many, many operating system upgrades. With very few exceptions, this has been the case with all IBM software -- across the board -- for over 40 years. So unless your site does something very unusual, there are no compatibility issues with moving from CICS TS 2.3 to CICS TS 3.2.
http://publib.boulder.ibm.com/infocente ... /index.jsp is the Information Center you need. You should bookmark this and refer to it as needed. If you click on the CICS TS document, then clicking Migrating, then in the right frame click on Migrating from 2.3, you can find the obsolete API elements (all BTAM-related CICS commands), changed API commands, and so forth. This will absolutely resolve all compatibility questions since this is the official IBM documentation on the subject.