Reminds me of one of the better touches in BvS, the early title card reading, "Metropolis: Mankind Is Introduced to the Superman." That "the" in front of "Superman" simply but effectively conveys a perception of him as inhuman, alien, a figure inspiring awe and fear instead of wonder and hope. It's not a portrayal of Superman I prefer, but it conveys the movie's tone very efficiently.
Cavill's is one of my three favorite Superman portrayals. It's a real pity that he's very unlikely to continue in the role.
The guy playing Supes on Supergirl is acceptable, but nothing to get excited about. He's got the good-enough-for-the-job-considering-the-pay vibe of the Tom Welling tribe.