While working in the archives, I recently came across this passage in the correspondence of Henri Bertin, French secretary of state, from 1773. He's writing about a potential Russian invasion of China.

As the Turkish war has shown, 12,000 Russians, because of how well-disciplined they are, are worth 30,000 Turkish troops, who are themselves no weaklings as soldiers; impressive in their height, their power, and their equipment, they proved unable to resist battalions bristling with artillery, resembling more walking fortresses than groups of soldiers (this story, I assure you, is not at all exaggerated) in a rage, aiming to exterminate humans in as large a quantity and with as much rapidity as possible, all of which is reduced to a principle whose execution is so precise that nothing can resist the violence and the continuity of the rolling fire which is certainly unknown in China. I understand that an expedition of 24,000 men would seem to the eyes of the court of Beijing as a vain effort by a power incapable of giving it any sort of concern with such petty means; but one should not doubt that the armies of China could be annihilated by this formidable artillery if they remain exposed to its fire for a few hours.

Notice the distinct lack of the "Asiatic horde" imagery that emerges full-scale with the Napoleonic Wars. Certainly some of that was being thrown around elsewhere, but to a much lesser extent than in the nineteenth century: the armies of most European countries were made up of the lowest and most desperate classes of society, so unlike the citizen soldiers of later eras there wasn't a lot of reason to think of them as quintessential embodiments of the nation.

There tended to be two levels of responses to Russian troops. The popular opinion was that the army consisted of vast hordes of cossacks with a sprinkling of European officers. This was a function of Russia's relative remoteness and Romantic notions of Eastern European wildness. Of corse, Frederick the Great also popularized the notion that tsarist troops were an undisciplined mass.

On a professional level, Western military and state officials tended to be highly impressed with the culture of its officer corps and the discipline of its troops. The eighteenth-century military theorist Henry Lloyd would write:

But that experience has proved that the Russian infantry is far superior to any in Europe, and. as their cavalry is not as good as other nations, reason dictates, that a mixed order of battle alone can conquer them.

The Saxon general Tielke would claim:

Russian regular troops yield to none in Europe to the point of exact discipline, and perhaps surpass, in this respect, most armies.

These estimates were partly a result of the fact that the Russian military was a professional force consisting of recruits who would serve in it as de facto lifers. When a peasant was drafted, his village would hold a funeral for him before he left as his new home was the army. In particular, the Russian artillery arm was quite large by most Western standards and added to the shock that Russian armies could be just as effective, if not more so, than Western and Central European ones.

Sources

Duffy, Christopher. Russia's Military Way to the West: Origins and Nature of Russian Military Power, 1700-1800. London: Routledge & Kegan Paul, 1981.

Lieven, Dominic. "Russia and the Defeat of Napoleon (1812-14)." Kritika: Explorations in Russian and Eurasian History 7.2 (2006): 283-308.

I don't have the sources on me right now, but I believe that the average Russian soldier was viewed with contempt. The vast regime and the numbers it could amass in terms of levies was feared. And the vicious Cossacks were also feared. The average soldier, however, was seen as second rate