White and black cores have identical hardware. The only difference is that the more recently manufactured black cores come from the factory with more recent initial firmware and TI WiFi chip CC3000 firmware revision.
Which TCPClient code are you trying to get working? Can you post your exact code?
Lots of times folks have forgotten that not reading the data out of the receive side of a connection will make the core memory overflow eventually and cause a fault (flashing red LED SOS code).
Some web code seems to need a
delay(20); after the final newline is sent for a HTTP GET request for reasons that are not yet understood. This issue has been captured over on github for the team to debug in the future.