It doesn't make much sense to compare the two books, as they (for the most part) cover different material. The bulk of Principles of Mathematical Analysis is devoted to a rigorous introduction to single variable and multivariable calculus. In contrast, Real and Complex Analysis covers measure theory, some functional analysis and Fourier analysis, and complex analysis.
Based on your description of what you want, I'd say you should start with Principles of Mathematical Analysis.
As for the style of the books, Rudin is famous for his "slick" proofs and difficult exercises. Some people like his books a great deal, and some don't. It might be a good idea to take a look at them (if possible) before buying one.