The difference between agile and waterfall in practice only is important in the first stage of the whole lifecycle, until the first delivery of the full product.
After that, what happens during the remaining lifetime of the system (usually at least 10 times as long as the initial development) can’t be described as such.
That being said, your question isn’t really clear. After all, “best”, “available” and “most widely used” are not the same.
– All development strategies are available.
– What’s best depends on the circumstances. The project manager decides.
– The pure waterfall method, as you learned until 1995 or so, is not used any more, I think, for any system of a significant size.