I can provide an answer to the question as it concerns the Russian Empire.

To start, let's not forget that a successful revolution most definitely did occur in holy mother Rus' but it was about 120 years later in the form of the February and October Revolutions of 1917. Both of these were actually quite similar to the French Revolution in some important ways, but you're asking specifically about the late 18th century.

After the abdication of the Emperor Nikolai II during the February Revolution (which actually occurred in March of the Gregorian calendar but the Orthodox Christian Russian Empire still used the Julian Calendar so it got that name instead), the political elite of the country headed by a cadet-branch descendant of the Rurik Dynasty (the imperial family which the Romanovs replaced in the 17th century) established the so-called Provincial Government which was truly answerable to a representative assembly parliament (called the Duma-- derived from the Russian word dumat' which translates "to think").

Nikolai II had established the Duma in 1905 (in response to another attempted revolution by the Russian people) with legislative veto (but importantly, not proposal) powers along with the October Manifesto the following year which granted certain basic civil rights and laid the groundwork for the authoring of the Russian Constitution of 1906. The 1906 Constitution revised for the first time in nearly a century the 46-volume Digest of Laws of the Russian Empire established in 1835 by Emperor Alexandr I (transliteration, not typo).

That essentially puts us in the Napoleonic Period and keeping in mind that the French Revolution is considered to have begun in 1789, the events in Russia between then and 1835 show why Russia did not experience a similarly successful uprising.

In 1789, Yekaterina II (The Great) was 27 years into her 34-year rule. This period is generally considered to be the Golden Age of Russia due to Yekaterina's embrace of Enlightenment ideals, wide-spread inoculation (similar to vaccination which appeared shortly thereafter) against smallpox, patronization of the arts, liberalization of education (she created the first state-financed institute of higher education for women, for example), issuance of government-backed paper currency, and plenty of other economic modernization reforms. In short, not a lot of domestic opposition to her rule.

The same cannot be said, unfortunately, for her son Pavel I who came to the throne when he was in his mid-forties and only held power for four years before be murdered in cold blood by a group of nobles (including his wife) from his own court in favor of his 24-year old son-- the aforementioned Alexandr I. Pavel was abjectly paranoid of the fate which eventually befell him and acutely aware of his vulnerability to overthrow in the vein of the French ancien regime. Anyone who proposed reform other than himself was denounced as a Jacobin.

One of Pavel's first moves as Emperor was to enact primogeniture succession (as opposed to the ruler-elected succession that existed in Russia at the time), and he moved to support every single war against Revolutionary and Napoleonic France which occurred during his reign. After his murder, countering Revolutionary France was also a major policy point for Alexandr I. In order to preempt any chance of widespread domestic unrest, Alexandr I instituted a few nominal liberalizing reforms, but considering Napoleon Bonaparte was an almost-constant adversary of Russia throughout his rule, and the French Revolution featured such indisputably hard-nosed suppression of religion (which was essential to the rule of the Russian monarchy), framing any kind of revolution at home as foreign-inspired was not the hardest sell either.

As to specifically why the Russian people did not overthrow their masters during the same time period, the short answer is that Russia (like all other divine monarchies of the time) saw the French Revolution for exactly what it was-- a warning to all of them that the masses could most certainly overthrow them given the right circumstances, so they acted accordingly, and suppressed anything that even looked like it might lead to meaningful reform all the way up until Nikolai II abdicated. One additional important detail to remember is that Napoleon's "whiff of grapeshot" on 13 Vendémiaire was seen as radical suppression of the Paris mobs. Massacring protesters was pretty standard issue crowd control in Imperial Russia-- including, but not limited to, the Copper Riot in 1662, the Bezda Peasant Revolt in 1861 and the Circassian genocide in 1864, Bloody Sunday in 1905, and the Lena Massacre of striking miners in 1912.