For me, it also depends. If I’m still not visual then I’ll leave the AP in, but I like to get a feel for the conditions especially because the 737 isn’t FBW. So if I’m visual it’ll be around 500-1000ft.
Here’s where the 737 shows its age. So on a single channel AP (only one AP engaged) if you push TO/GA once it will give you that 1000-2000fpm rate of climb, however, the AP will disconnect (bizarre I know). If you’re doing an autoland, both AP’s need to be engaged and therefore if you hit TO/GA, the AP will remain engaged.
So the go around will be a half manual procedure, unless you have disengaged the autothrottle at the same time you disconnected the AP. In which case you will need to push the thrust levers up to the target N1 manually at the same time as watching the pitch attitude and lateral tracking.
So it works like this (assuming automatic flight at GA):
PF will push the TO/GA button, the thrust levers will come up to achieve a 1000-2000fpm rate of climb, the AP disconnects. PF will pitch the nose up to 12° and trim like crazy. There’s a lot of back pressure because of the thrust coming from the engines. At the same time the PF will call GA Flap 15. The PM will select the flap to 15 and call positive rate, the PF will confirm and call gear up check thrust. The PM will then confirm that enough thrust is set to achieve the minimum rate in this case.
Once everything is under control the AP can be reengaged and you can take a quick breath.
So as you can see very different and much louder than a modern airliner.