Answer Set Programming (ASP) and Constraint Logic Programming over finite domains (CLP(FD)) are two declarative programming paradigms that have been extensively used to encode applications involving search, optimization, and reasoning (e.g., commonsense reasoning and planning). This paper presents experimental comparisons between the declarative encodings of various computationally hard problems in both frameworks. The objective is to investigate how the solvers in the two domains respond to different problems, highlighting strengths and weaknesses of their implementations, and suggesting criteria for choosing one approach over the other. Ultimately, the work in this paper is expected to lay the foundations for transfer of technology between the two domains, e.g., suggesting ways to use CLP(FD) in the execution of ASP. 1 Copyright © 2007, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.