For the best primary source see Polybius:
http://www.fordham.edu/halsall/ancient/polybius-maniple.html
Polybius was not some Ivory tower theorist either.
The last three paragrtahs preety much sum it up:
/quote
For no speculation is any longer required to test the accuracy of what I am now saying: that can be done by referring to accomplished facts. The Romans do not, then, attempt to extend their front to equal that of a phalanx, and then charge directly upon it with their whole force: but some of their divisions are kept in reserve, while others join battle with the enemy at close quarters. Now, whether the phalanx in its charge drives its opponents from their ground, or is itself driven back, in either case its peculiar order is dislocated; for whether in following the retiring, or flying from the advancing enemy, they quit the rest of their forces: and when this takes place, the enemy's reserves can occupy the space thus left, and the ground which the phalanx had just before been holding, and so no longer charge them face to face, but fall upon them on their flank and rear. If, then, it is easy to take precautions against the opportunities and peculiar advantages of the phalanx, but impossible to do so in the case of its disadvantages, must it not follow that in practice the difference between these two systems is enormous? Of course, those generals who employ the phalanx must march over ground of every description, must pitch camps, occupy points of advantage, besiege, and be besieged, and meet with unexpected appearances of the enemy: for all these are part and parcel of war, and have an important and sometimes decisive influence on the ultimate victory. And in all these cases the Macedonian phalanx is difficult, and sometimes impossible, to handle, because the men cannot act either in squads or separately.
The Roman order on the other hand is flexible: for every Roman, once armed and on the field, is equally well-equipped for every place, time, or appearance of the enemy. He is, moreover, quite ready and needs to make no change, whether he is required to fight in the main body, or in a detachment, or in a single maniple, or even by himself. Therefore, as the individual members of the Roman force are so much more serviceable, their plans are also much more often attended by success than those of others.
I thought it necessary to discuss this subject at some length, because at the actual time of the occurrence many Greeks supposed when the Macedonians were beaten that it was incredible; and many will afterwards be at a loss to account for the inferiority of the phalanx to the Roman system of arming.
/quote
This is something of a simplification though. In fact historically a properlly handled Macedonian style "combined arms" army such as that of Phyrus and (very probably) Hannibal were able to defeat Roman Republican Armies. It wasn't until the Roman system evolved to the manipular system (popularly refered to as the Marian reforms) and added a larger perecentage of more professional cavalry and skirmishers that it became a superior system as described by Polybius.
Even before this it did have one major advantage that Polybius may well have understood but foreborne to mention: it was much easier to lead. Macedonian combined arms operations require good command and control, excellent timing and a good understanding of how to use all three arms of your army. Roman strategy (especially during the Republican era) was usually the simple application of Roman tactics i.e. steam roll the enemy.