Were the Spartans as effective of a military force as they are often portrayed in popular culture? How did their tactics and training actually compare to other contemporary empires?

You may want to check out previous threads on the subject here:

The gist of these being that the Spartans have been catapulted into fame by non-Spartan Hellenes who loved to romanticize their qualities. Philosophical opinions from antiquity admired the Sparta which never existed because it fit into ideals of a virtuous state of free citizens (nevermind their massive slave population which they rode over roughshod). The myth of the Spartiate supersoldier is a bad pop history trope that has survived for thousands of years until, as you know, it reached its apotheosis with a half-naked Gerard Butler and Michael Fassbender killing rhinos and horses with their bare hands.

In summary, they were an incredibly stable but stagnant society which fielded a well-trained, disciplined army which trained longer and harder than other Hellenic states, but they were by no means invincible.