PDF is NOT a Turing-complete programming language. One of the main reasons for creating the PDF format is precisely that this "feature" of PS was considered a bad idea. PDF is a static description.
Secondly, PDF is by no means a variant of PostScript targetted towards on-screen viewing. PDF has been designed for all sorts of target devices: professional printing devices, pre-press work and also for on-screen viewing, but the latter is no more the focus of PDF than any other target. You could call PDF an extensible, object-based, static (i.e., NON-Turing-complete) variant of PostScript with additional structure imposed to allow random access to objects. If Adobe were to design it today, I doubt it would look much different.
PDF could be called less static than Draw (because it does not require each and every attribute to be specified for each object, but instead keeps a "current graphics state"), but the contents of a PDF page are still a sequence of graphical objects, just like a Draw description. It is also significantly more complex than Draw, simply because it does so much more and needs to support all sorts of professional printing features. Finally, it is stream-based, which makes it more difficult to manipulate, but this is the price you pay for all the flexibility.