Answer: if the aircraft can not climb at 1500 fpm or more a climb instruction will not be issued.
However my question is still of interest, and what if BOTH are limited by this constraint.
How would you design the TCAS to handle that situation? You would advise one aircraft to not descend, while advising the other to descend at 1500 fpm. If that doesn't provide enough margin, then advise increased descent of 2500 fpm.
The plane's max altitude at which 1500 fpm climb can be achieved is determined by the aircraft maker, and programmed into the TCAS processor. That altitude is pretty low in a 747-100 in partial flaps configuration.
GB