Both Steven Weinberg's "The Quantum Theory of Fields" and Edward Witten's "Quantum Field Theory and the Jones Polynomial" are highly regarded resources in the field of theoretical physics, but they serve different purposes and target different audiences.
Steven Weinberg's "The Quantum Theory of Fields" is a comprehensive and authoritative three-volume set that provides a detailed and rigorous treatment of quantum field theory. It is aimed at advanced graduate students and researchers in theoretical physics. Weinberg's book covers a wide range of topics in QFT, including the formalism, symmetries, renormalization, and gauge theories. It is known for its mathematical rigor and depth of understanding. It is an excellent choice for someone looking for a thorough understanding of quantum field theory.
Edward Witten's "Quantum Field Theory and the Jones Polynomial" is a more specialized text that focuses on the intersection of quantum field theory and mathematics, particularly in the context of topological quantum field theories. It is targeted towards mathematicians interested in gaining insights into quantum field theory and its relation to mathematics, specifically the Jones polynomial and its applications. While it does cover some foundational aspects of QFT, it may not provide the same level of depth and breadth as Weinberg's three-volume set for someone primarily interested in the broader field of quantum field theory.
In conclusion, if you are a theoretical physicist looking for a comprehensive understanding of quantum field theory across various topics, Weinberg's "The Quantum Theory of Fields" would be a highly recommended choice. However, if you are a mathematician interested in the connections between quantum field theory and mathematics, particularly the Jones polynomial, Witten's "Quantum Field Theory and the Jones Polynomial" would be a more suitable option. Ultimately, the choice depends on your specific interests and background.