Chapelton

Honestly it really depends on when you look at each, both have had huge pluses and minuses. However if we are to look at them from their golden ages and at their top strength (which is how I prefer to look at each warrior culture) then the Roman Empire was probably the best of the Ancient Empires. Something that Rome excelled at that other civilizations failed at was (up until the end) adaptation. Romes greatest strength was get this CULTURAL APPROPRIATION ;p they went in disrupted and area, conquered it and then took what was useful to them,. Tech, information, slaves, tradable goods, etc… then they brought it all back to Rome figured out how to make it better and shipped it out to the rest of the world. Probably some of the first cases of reverse engineering we see historically (that immediately come to mind).

As for the Legions

They were a fantastic organization and adaptation on the then traditions of combat and military. After the Marius Reforms they became a truly imposing military power. Using (at the time) cutting edge technology, and recruiting the first real professional (contracted) army of its age. They signed troops up for 20 year stints, and upon your retirement you could either rejoin under a special unit of veterans where you had prestige, and lessened duties, or retire and receive land of your own in the boarder lands. This was brilliant of the Romans for any number of reasons, but long story short it gave the boarder lands and other freshly conquered territories additional troops, and Romans if the locals were to ever rebel, who owed their loyalty, and land to the Empire.

The Romans also organized their military very well, splitting it into squads (tent parties), platoons (century), Companies (cohort), and Division or regimental levels (Legions). They invented essentially the modern military, and we use much of their wisdom and knowledge ever to this day. 

Legions were able to operate independently of each other or in concert to achieve goals and persecute the foes of the Empire. The Roman legion changed the rules of warfare in many ways, they built roads and other public works as they went so that future generations or missions could move quickly through Roman territories. And instead of making camp each night Romans would actually make fortifications, digging ditches, filling moats, placing spikes, etc… in order to protect their camps from attack and subterfuge.

Roman Legionaries carried most of their tools and weapons with them on the march freeing up wagons and slaves for provisions, siege equipment, etc… A few things to note about the Roman Legionary are the (more or less) full armor, the tower shield, and the javelin (each Legionary was issued 2). These were of the utmost importance to Roman dominance in the region as its soldiers were far better protected than its enemies, and that its soldiers had both ranged and melee availability. As the enemy closed on a Roman legion  or vice versa the Romans would throw their javelins’ (specifically designed to twist and bend on impact, meaning that even if it didn’t kill you it twisted inside you making it harder to remove and more likely to incapacitate you for a kill).

The Roman Legionary himself was a less than impressive one on one specimen but a well disciplined soldier none the less, who followed orders and worked well as a unit. They were master engineers, Caesar once used his legions to besiege a city by surrounding it with a fortified wall. And when an enemy army threatened to encircle his forces Caesar built a second wall to defend his siege. Using the engineering brilliance of the legions and their construction expertise he defeated the might of all Gual (outnumbering him several times over). 

All in all the Roman Empire and Legionary at the hights of each were fantastic, and you should do more independent study on each. Much of our modern day is based off of aspect and inventions of the Romans.