ETA is owned by Swatch group, which owns a ton of watch brands[1], including Hamilton, which I would say competes head-to-head with the most Timex pieces (at least in the $500 price range).

There are other Swiss automatic movement makers though, like Sellita (the SW200 is basically an ETA 2824[2]).

1: https://www.swatchgroup.com/en/brands-companies

2: https://www.christopherward.com/etasellitastory.html