The level of morale in a conscript army is usually lower, but it's not always that low, and it's not often less than required. For example, WW1 wherein every army began as a conscript army (excepting Britain, which later turned to exactly that). The conscripts of these armies lasted around 2-4 years in the worst meat-grinders in military history before serious dissent ever reared its head - and then it was less due to time or the conscript nature of the army as that casualty rates for combat units had hit 100% or over (a rough guide to when the army revolted in some form). At that point, soldiers were just exhausted by all the death, and a disproportionate number of the dead were the bravest who wouldn't have revolted. The only exception to this was the Germans, who held out the longest and beyond that casualty rate, probably because they were fed on a diet of victory throughout the war. Moreover, Napoleon's Grand Armee was a conscript army - and no one would claim that wasn't a well-oiled machine.
People looking at Vietnam have turned a special lesson in conscription's use into a general one. Conscript armies aren't necessarily bad or cowardly; they just aren't good or brave when the citizens (and thus the soldiers) don't believe in the cause. Professionals are more likely to suck it up (because they're a bit more patriotic than the average joe).
There are trade-offs involved in any military system. A professional army, conscription, citizen militia, mercenaries - all of them have their pros and cons. For example, a professional army is well-trained; but it is also a powerful force that is essentially disconnected from the citizenry. You only have to look around the world, or at history, to see dozens of examples of professional armies that launched a coup on government. This usually happens when a soldiery is less loyal to its system of government than its military leaders. Professional armies, therefore, are death sentences to countries with weak governments, little civic feeling and constant land war. Britain, America, Canada and Australia have managed to keep professional armies on a politically tight leash because of a sense of patriotism which trumped loyalty to military; and because none of them have suffered especially long periods of sporadic wars since the inception of professional armies - a destabilising effect that creates a greater love for the military than usual. (When foreign armies are marching across your borders every few decades wouldn't you value the military a bit more?)
The costs of conscription are quite costly though. They can include low morale and training but not necessarily. They do include a massive drain on the economy of a country, such that in a long drawn out war the conscript powers will collapse. This is the lesson the world only learned in World War 1. Before then, Europe had looked at Napoleon's success and concluded that conscription was the solution to the problems that had dogged the other systems. When WW1 came around, though, it was seen what escalation would do: a long struggle that drained a country until total collapse (Germany, and not Britain or France by luck and the Lusitania).