The most common mistake is to think go-around at minimum and go-around at 1000ft involve exactly the same procedure.
At minimum, there is no question, you have to go TOGA and do the rest of the actions immediately, otherwise you'll bust the minimum. But at 1000ft if you are either unstabilised or ordered go-around from ATC, you can take a deep breath, verify missed approach altitude is set, review go-around procedure and do it slowly without any rush.
As far as the TOGA vs. LVL CHG goes, I'd always go with TOGA below 2000ft RA - the only exception being if I'm very close to missed approach altitude (e.g. go-around from 1800ft with missed approach altitude 2000ft). As said, this is the easiest way to get out of approach mode and this is what most of your colleagues expect.
Let me further break down what his opinion was at level of around 1000 AGL it is more than sufficient to use LVL CHNG rather then TOGA since the missed approach altitude might only be be say 2000 or 3000 AGL (airmanship was the word he used)
Airmanship means that you also understand the aircraft you are flying and its systems. Funny story, LVL CHG with CLB thrust at flaps 15 in a very light aircraft will result in a much greater vertical speed than TOGA (which is limited to 1000-2000ft/min unless you press it twice).