I've now done enough experimenting to determine:
<>Starting with new, blank media, everything seems to work properly on the new computer.
<>Adding another session to disks created on the old computer loses everything beyond session 1.
<>Session 2, 3, ... could be read on the new computer before an additional session was added; after adding a new session, only session 1 can be read.
<>CDBurnerXP sees all the files of all the sessions, but Windows Explorer sees only session 1.
<>CDBurnerXP does not seem to be able to do anything with the files except list them.