First, when I asked before about Metropolis I suspected--but didn't know for sure--that the trippy anime of that title which I watched a year or two ago in a half-asleep stupor was an adaptation of the 1927 film. Your description was familiar enough to me to confirm that it was, although Wikipedia say it's a very loose adaptation.

Also, I'm pleased to have learned a new word tonight, which I can foresee myself using in the future: bromance. Yes, that will be a good one to add to my personal lexicon. :)