The Spartans were hand-to-hand/close-in combatants. They excelled in it and this is what they were known for. In fact I remember a story about a Spartan boy who stole a fox and hid it beneath his cloak when he was confronted by the owner. Rather than letting the theft be discovered, he allowed the fox to gnaw and scratch him without showing any signs of pain while being questioned. He was let go by the owner and the boy later died because of the wounds if I recall. Had he been caught because of showing any pain, the disgrace would not have been in the stealing, but because he showed he was in pain. He would have also been severly whipped.
Tough bastards I give you that, but don't believe everything the movie said. Most of it was exaggerations.
First, babies were inspected by a committee of elders, not one man as shown in the movie, and if considered too weak they were left to die by exposure on the sloped of Mount Taygetos. There was no 'dead baby pile' as shown in the movie.
Also, there was no Spartan gold like when shown in the 'oracle' scene. Point of fact was Silver would have been used if anything, not gold. Real life spartan authorities refused to adopt the system of making silver into coins like the other Greek cities. Instead they used iron bars for money. Try to immagine the king throwing down a bag full of iron bars instead of gold. Yeah, I chuckled a little at the thought too.
Sparta also had two kings, not one, and the kings were not the end-all-be-all power in Sparta. Actually, the people elected 5 elders to watch over the kings and make sure they were held in check. Two elders always went along when a king went out to battle, they handled the diplomatic affairs and could fine or arrest a king if he got too full of himself. Of course the movie couldn't have worked if history had been accurately followed so I give it some leeway here.
Now in real life, when war came to Sparta the Spartan officers relaxed the discipline a bit and allowed their men to beautifying their hair, armor, and their clothing. It was said the men looked like horses prancing and neighing before a big race. They exercised the men less and allowed the men to 'chase tail' (and yes Spartans were 'boy lovers' too, in fact they had institutionalized pediphilia) if they wished. All this was done so that war itself was a rest from the preparation for war.
Many stories from those who fought the Spartans agree it was impressive and frightening see the Spartans advancing in time to a military song played on a flute, calmly and cheerfully moving into the dangerous battle to the sound of music...smiles on their faces. It was unnerving to many enemies to see this. We kind of saw this in the movie, minus the happy-go-lucky flute music.
Spartans were fierce warriors, no doubt. Alexander the Great never went up against them, respecting the knowledge that any confrontation with them would result in heavy losses... but think on this. By 362 BC Sparta's role as the dominant military power in Greece was over. The Thebans under Epaminondas defeated Sparta in 371 BC and so ends Sparta power in Greece. They still were fierce fighters but their height of power was over.
Flash forward 225 years to 146 BC. All of Greece was conquered by the Roman general Lucius Mummiusm, including Sparta. During and after the Roman conquest, Spartans were allowed to continue their way of life. The city became a tourist attraction for the Roman elite in fact.
As for Sparta vs Rome around 170-180 A.D. (when Maximus was in power as a general...being that 180 is when Emperor Marcus Aurelius died and is also the end of the Marcomannic wars which we saw at the start of the movie.)
First off, the Thebeans defeated Sparta back in 371 BC. These are armies using the same technology as the Spartans, were able to defeat the Spartans on equal footing.
Move forward to 146 AD. Rome, with superior weapons, armor, and tactics beats the Spartans along with the rest of Greece.
Now you want to pit the Spartans against an enemy that already has defeated them but give that enemy 300 to 330 years advancement of military tactics, training, and weaponry?
I can respect Spartan training but this would have been a slaughter in favor of the Romans.
This is like asking who would win, the US military of the Civil War or the US Military of WWI? (and that is only 50 years or so difference)