Solving the Traveling Salesman Problem (TSP) consists in finding an optimal Hamiltonian Cycle in a graph. In the TSP with Time Window constraints (TSPTW), each node of the graph is required to be visited during a given time interval. The TSPTW has recently received a lot of attention and has been considered under a variety of objective functions, e.g., makespan, travel time, or tour duration. Due to (i) the variety of solving approaches available and (ii) limitations of existing benchmarks, it remains relatively unclear which types of approaches perform best under which conditions and performance criteria. This abstract presents a work in progress focused on the makespan and travel time objectives: we experimentally compare a variety of solving approaches and paradigms, including our adaptation of existing solvers to a new objective. We perform this comparison on both classic benchmarks and on a new benchmark we generated based on a recently published model aiming to address some of their limitations.