STR-LHR on BA will come into T5, STR-LHR on 4U comes into T1 (not sure if they plan to move to T2 or not). According to the LHR site, as of now, Air NZ uses T1, although I surmise they'll move to T2 with the rest of the *A carriers at some point.

Another thing to consider is baggage allowance; I would check both.

As far as the connection, do you plan to check baggage? Also, if making a landside connection, you'd need to clear passport control, collect baggage (unless checked through) and then make your way from T5 to T1/2...this could take time. I would not plan on BA transferring your baggage to NZ.