Why were the Russians more able to invest in their army than the Ottomans? Were they more efficient in taxation than Ottomans? Did they spend less on non military than the Ottomans? And what factors kept the Ottoman Empire from adopting the arms of the Russian Empire?
Well, importantly, Russia was a much larger state, in terms of size, and population, and available resources to exploit. That doesn't always translate exactly into revenue, and nobody would call eighteenth-century Russia's government an extractor of national wealth of the same efficiency as Prussia, let alone Britain, but they were starting from a much-improved position relative to the Ottomans. Russia could spend more money because Russia
had a lot more money.
Some macrohistorical explanations of declining state power in Muslim Southwest Asia over the course of the eighteenth and nineteenth centuries have tried to highlight taxation as becoming less efficient in relative terms due to Christian conversions to Islam, which supposedly reduced direct tax revenues while increasing the pool of available military manpower, but the problem with that is that the
jizya and its successor, the
baddal-askari, don't track particularly well with any decline, relative or absolute, in Ottoman finances and military power. (Admittedly, many of these statistics are estimated, because sources are so poor. That cuts both ways, of course.) Similar things like an ostensible lack of customs tax revenues due to the existence of the capitulation agreements with Western powers are also hard to directly connect to revenue difficulties, especially balancing that with the massive amount of funds that Ottoman sultans of the nineteenth century were able to borrow from European powers. It's true that Ottoman tax revenues didn't increase at the same rate as Russia's did over the course of these centuries, but neither did the Empire's population, which was already smaller than Russia's by the late eighteenth century by a few millions and which by 1900 was 20% of Russia's.
Part of the problem here is that the causation lines are difficult to draw, here. It'd be a nice story if one could draw a line between the Agricultural Revolution and Russia's increased population allowing the Russians to inundate the Ottomans with troops and cash. But it'd also be a story that is probably wrong, because the Agricultural Revolution's technologies didn't take off in Russia until later, in the nineteenth century; Russia's population and economic growth in that century was probably more due to the settling and clearing and planting of Ukraine than to technological improvements, although both were factors; the course of any individual war militates against claiming that Russian manpower superiority
won them any individual conflict, but rather that it helped create a favorable matrix for doing so, insofar as it was correctly applied; and so on, and so forth. Russia's population
did meaningfully grow over the course of the eighteenth century, but was there some sort of tipping point that made regular victories in wars more easily thinkable? No.
A similar problem occurs when one considers Ottoman military technology. The usual narrative is that the yeniçeri stranglehold on the Ottoman military, and yeniçeri obscurantism, prevented the Ottomans from adopting modernized European military arms and forms of organization. Which is true, to an extent - the yeniçeri lodges did often react against modern equipment in all its forms - but has been overstated. And it's not as if the destruction of the yeniçeri forces in the Auspicious Incident of 1826 automatically made the Ottoman military better. The infant new-model army was born in the middle of the war against the Greek rebels, which was in large part being subcontracted out to the Egyptian military, and within a few years had to deal with a Russian invasion that, after initial setbacks, resulted in a campaign of maneuver in which the Russian commander outmaneuvered his Turkish adversaries and was able to dictate a peace in Edirne. And, of course, the yeniçeri were never the entirety of the old Ottoman army, which included large numbers of irregular levies and provincial formations, and many of those forces persisted under the New Order (
Nizam-ı Cedit), further limiting the extent to which we can place the burden of Ottoman military troubles on the yeniçeri.
I suppose the point I'm trying to make is that you're asking questions that, in large part, require Big Answers, but a lot of history as it is practiced today militates against giving a lot of these Big Answers because there are few narratives that do not go unchallenged by individuals who make close studies of more narrowly defined areas. A narrative isn't very useful if it doesn't describe the facts of specific situations as we understand them. So, again, luck and contingency were highly relevant and placing the burden of the explanation on things like "Russia was more populous and therefore wealthier" is not totally right, but also, admittedly, not totally wrong.
It's a wishy-washy answer, I know, but it's easy enough to demolish answers that are more specific and confident.