I guess this is an old topic, but it sparked my interest.

 

I'd take Alexander hands down. In the fourth century, Rome was still emerging as a power on the Italian peninsula, they were just figuring out the basics of the legion. They would've given Alexander a tougher fight than the Persians, and if they had good terrain to negate the Macedonian cavalry, they might have even one a battle or two. But they weren't strong enough yet.

Legions as you refer to them did not exist prior to the Marian Reforms which occured around 107 B.C.  Alexander would have won handily.  The Roman military at that point existed as a tiered system:

 

Going from lowest to highest they were:

 

Militia- used hoplite tactics

Velites - skirmishers- no armor, had a small sword (gladii) and lots of javelins. 

Hastati-Lowest of standard infantry: typically poor, had to supply own equipment (large shield, light armor) used a spear and later a sword as well as a pilum

Principes-Armed in the same way as Hastati but typically wealthier so their armor was better

Triarii- Another step up: wealthiest of the army, armed with spears, heavy metal armor, large shield

 

Cavalry:

Equites- Roman Cavalry was typically not very good and were done away with in favor of foreign auxilaries around 88BC

 

Typically they fought in a phalanx like formation in three tiers organized from lightest up front to heaviest up front.  They did not begin to fight using Maniples until the 3rd century BC, after Alexander. 

 

With the Roman military organized how it was and how good Alexander and his army was he would have absolutely won against Rome barring some massive mistake