The subscription services aren’t going to have many recent movies. If it’s recent, you’re most likely going to need to rent it from a service like Vudu, Fandango, Google Play, etc. Amazon also lets you rent movies even if you’re not a prime customer.
I personally like the way Amazon Prime allows you to find other movies based on one movie. Amazon will suggest other movies similar to that movie, and you can also see what other customers who liked that movie also watched. I’m not sure how to do that with Netflix. Netflix makes it’s own suggestions. Another advantage is that Amazon often has the theatrical trailer, which is useful to decide if a movie is worth watching. The trailer is often missing on Netflix.
I usually use external websites to find movies to watch on Netflix. Find sites that have “best movies on Netflix” and “new to netflix” to find some things to check out.
I’m disappointed that Netflix doesn’t make some of this easier. It seems their model is “We know what you want to watch” rather than “We’ll help you find something to watch”.