Not OP either, but there are many different aspects to solvers that make them useful in different situations.

For example, I would perhaps not use the same solver for a best-effort problem where I can program strong heuristics, vs a problem that must be optimized and no natural heuristics exist. Sometimes problems have a natural type of formulation, and it is best to use a solver for that type of problem (linear programming, mixed integer programming, SAT, pseudo boolean, constraint programming, ...).

Choosing a solver also very much depends on the deployment situation; how should a model be used and what operational concerns are there.