Quantum Phase Estimation (QPE) is one of the key techniques used in quantum computation to design quantum algorithms which can be exponentially faster than classical algorithms. Intuitively, QPE allows quantum algorithms to find the hidden structure in certain kinds of problems. In particular, Shor's well-known algorithm for factoring the product of two primes uses QPE. Simulation algorithms, such as Ground State Estimation (GSE) for quantum chemistry, also use QPE. Unfortunately, QPE can be computationally expensive, either requiring many trials of the computation (repetitions) or many small rotation operations on quantum bits. Selecting an efficient QPE approach requires detailed characterizations of the tradeoffs and overheads of these options. In this paper, we explore three different algorithms that trade off trials versus rotations. We perform a detailed characterization of their behavior on two important quantum algorithms (Shor's and GSE). We also develop an analytical model that characterizes the behavior of a range of algorithms in this tradeoff space.