PageRank is one of the most important ranking techniques used in today's search engines. A recent very interesting research track focuses on exploiting efficient numerical methods to speed up the computation of PageRank, among which the Arnoldi-type algorithm and the GMRES algorithm are competitive candidates. In essence, the former deals with the PageRank problem from an eigenproblem, while the latter from a linear system, point of view. However, there is little known about the relations between the two approaches for PageRank. In this article, we focus on a theoretical and numerical comparison of the two approaches. Numerical experiments illustrate the effectiveness of our theoretical results.