Which is better for strength training: large fitness equipment or my body weight?

Neither one nor the other. I believe that there is no good or bad about any kind of training but there can be a mismatch between the modality used and the person using it.

While I firmly believe that people should learn to control their own bodies, there can be many paths to that end, body weight training, machines or free weights all being possible means to an end.

Which path ultimately is the one you choose depends on your goals and inclination, and it does not even have to be an either – or.