Obviously both will exist and compete with each other on the margins. The thing to appreciate is that our physical world is already built like an API for adult humans. Swinging doors, stairs, cupboards, benchtops. If you want a robot to traverse the space and be useful for more than one task, the humanoid form makes sense.

The key question is whether general purpose robots can outcompete on sheer economies of scale alone.

I mean, I would take a robot to handle all of my housework.

Purpose built, that probably takes the form of a humanoid robot since all of tasks it needs to do were previously designed for humanoids.