Did any nation have a demonstrable qualitative advantage in their soldiers of the 18th century, and how did they achieve this?

The Hessian soldiers (see The Best Armies Money Could Buy) were widely recognized at the time as the most elite in the world (which is why the British hired them). This was because of their discipline, tactics and good use of equipment, not so much their marksmanship. The best shots in the world until quite recently have always been Americans by a long shot (no pun intended).

In military theory 18th,19thC a firefight was a line of men robotically shooting and advancing in unison against the enemy till putting them to flight with the bayonet.The reality rarely, if ever matched. In the stress of battle a soldiers natural reaction is to blaze away aimlessly, hoping the noise discourages the enemy then run if they keep coming anyway; only direct control by officers can prevent this.

Contemporary evidence from Albuera (1811) have the British soldiers 'constantly advancing on & shaking the enemy'. Yet the firefight was at some 80 yards range and lasted around 20 minutes. Clearly the advances were small & fitful - but they did occur & only on the British side.

A look at the numbers and organisation of officers in a firefight reveals that the British not only had the best ratio of officers & NCOs to men, but they were positioned where they could best control and encourage the men forwards. No other army came close at the time, and consequently the British (at the unit versus unit level) had a superior reputation.

Obviously factors of logistics,training, and generalship come into play for winning battles - but the basic determinant of the troops reputation was management organisation.

The English army under Marlborough in the War of the Spanish Secession was of very high quality (1704-1714) and brought Louis XIV to the brink of ruin. The march from the Netherlands to Bavaria to meet the French at Blenheim was a masterstroke of marching and logistics, and they destroyed the army they met in battle.

Probably the major reason why is that its relative smallness led to it being able to be something of an elite force and it could choose its battles. The relative wealth of England probably helped it be equipped to a high standard.

Of course, the English historians will go on and on about this in every war before and since, but in general English troops have been high quality since the Hundred Years War, if a bit small in number. When they plump out in WWI/II the luster fades somewhat, but they have made it through regardless.

Performance on the battlefield is often about tactical organisation and method, rather than equipment and individual skill. Musketry was on the whole massively ineffective.

Prussia had better tactical organisation during the Frederick the Great Period, but relatively short lived, The French were generally better after that.

I know Napoleonic period is little after the 18th but Nosworthy is a good back about tactical doctrine and effectiveness of musketry. http://www.amazon.com/Battle-Tactics-Napoleon-His-Enemies/dp/0094772401

Makes the argument that British fire doctrine of with holding fire until the enemy were a point blank (on attack or defence) made it much more effective (both in casualties and moral) That and better awareness of "levelling" (how high to aim ratline to distance from the target) than individual skill of the British with the musket.

Short answer:

Yes, but one army did not have an edge over the entire century. A century, at that time, was nearly three generations. And militaries of the time could only serve for a small timeframe, so you could have up to ten different generations in one army for this century.

Long answer:

During the 18th century, in Europe, armies were in a very subtle situation. Different factors led them to be of quality and efficiency. I will concentrate on Western Europe since there has been a variety of situation in the East of Europe (East of Prussia), and the South (South of Austrian Empire).

Some of the factors were as follow:

• More training and skill management

In Europe, after state built themselves during the end of the Middle Age, they had started to fight for a variety of reasons. But the main point is they moved from the mercenaries of 16th century into government's armies. This led them to manage skills of their soldiers: training included drill, tactics were written, and officers slowly started, during the 18th century, to attend to military schools.

• Fast weaponry evolution

During those centuries, and especially during 18th century, musketry, rifles, and artillery had major technical evolution. This came from the actual manufacturing of the weapon to better logistics and new tactical possibility with faster loading and firing (especially for artillery). I am not aware of technical evolution for cavalry, but the development of lighter firing weapons led to mounted rifles and dragoons. All of these evolutions needed to be appropriate by soldiers, and some were only during Napoleonic Era. But the point is that different countries had different innovations at different time, so the resulting quality of their armies was varying fast.

By the way, this has been also true for navies, but I won't speak of that there.

• Officers changed. Kings changed

Remember: this was not a time for meritocracy, there was still a lot of noble people who managed to get into military responsibilities for who they were born, and not for what they were able to do. But failure is a failure, and sometimes king and ministries changed their mind and dismissed commanders. This is not to say that officers were always stupid men, some of them were truly capable. But this is to say that the quality of commanders could change fast, at top as well as lower commanding scales. As a result, the quality of a given unit could change and could be more or less well used by high command.

• Economic system

At the time of the 18th century, centuries of war in Europe had built social identities. John Keegan quoted some of the "military people" of Europe in his Battle of Normandy. For example:

• Scottish
• Swiss
• Different Germanic people such as the Hessians
• Prussia, as it developed a fairly big army compared to the size of the state
• Cossacks
• etc...

Those people ususally provided units to larger countries, as mercenaries or as regulars, such as United Kingdom, Austria, Russia, and this resulted in different quality in one country's army.

This site implies that the redcoat was given a higher allowance of live ball shot than other nation's soldiers, however the source is not stated. An Osprey book confirms the figures for the British army though, although there is no information provided for the state of the other armies.

I can address your confusion in latter part at least.

According to Maddison, The UK's GDP passed France's sometime between 1700 and 1820 and Spain's by 1700. According to Bairoch, England's GDP passed France's between 1830 and 1840 and was far past Spain's by 1800 (when his numbers start).

So at the absolute least, it appears the UK's economy was doing better than Spain's during the 18th century, and was in the same league as France's.

As for their relative military performance, I'd argue that its more a matter of inclination than money. Scarcely 100 years earlier, tiny Sweden (with a tenth of the UK's GDP at the time) was a big-time military power in northern Germany, with arguably Europe's best army.