Both are correct, but it really depends on the context for which one you would use. Technically, they’re interchangeable, but there are times when one is better than the other.
For example, if there was a movie in theaters and I wanted to tell my friend that it was playing right at that moment, I would say: “It is playing now.”
However, if I wanted to see this movie and I knew it was in theaters but I didn’t know the times, I would say: “It’s now playing in theaters.”
Watching now and now watching are interchangeable, but again, it depends on the context.
For example, if I wanted to say that I had been watching something else previously but I am watching something different at this moment, I would say: “I was watching that movie, but this movie is what I am watching now.” However, it sounds more natural to say: “I am watching this now.”
If I wanted to say the same thing in different words, I could use ‘now watching’, but it goes somewhere else in the sentence. I would say: “I was watching that movie, but I am now watching this movie.”
I hope this helps! :)