An explanation can be made if we presume, as I've written before, that the Russian authorities don't have anything personal against Estonia, but rather just need a target for discontent among the population. Be it Estonia, Georgia, Moldova, Ukraine, or Burkina Faso.
It's true that the argument of Estonia's successful democracy being a threatening contrast to Russia's totalitarianism doesn't hold water: Russia is far from caring what anyone else thinks of it. Russians will enjoy it if their country is feared, but don't especially need for their country to be liked.
Now, let's remember that when Georgia was under fire, it was far, far worse than the height of anti-Estonian sentiment. Deportation of Georgian citizens, registration of people with Georgian last names, a threat of interrment... All Georgia did was elect a new president who was publically Western-minded* and unfriendly to Moscow. The same thing happened in Ukraine. I'm not really sure what caused the ban on Moldovan wines - I'm just going to take my own advice there and presume it was the Russian Surgeon General's stupidity rather than anyone's malice.
But Estonia didn't go through such a major shift - it was clearly Westbound from the beginning. While it was never particularly friendly with Russia, most of the time it wasn't an important enemy. So the ire of Russians was not caused by a sense of betrayal (not that this isn't there, in a perverse form, but that's a topic for another article).
So what is the difference between Estonia and Finland?
The answer is: exit points. On an emotional level, Estonia is felt to have been lost recently, in '91; most of the population of Russia today remembers a time when Estonia was their own territory. On the other hand, very few people alive now remember Finland as a Russian province; while Russians may know factually that Finland was a province of the Empire, it has been a Western country for the entirety of their conscious existence.
And here's the interesting thing. Both Finland and Estonia gained their independence and then made good, grew their economy and living standards, have become distinctly better than Russia on an everyday, obvious level. The difference is that Finland escaped from the Tzar, whereas Estonia escaped from the Secretary General.
Thanks to Putin's bridge to Soviet propaganda, which was entrenched in the consciousness of regular Ivans, a massive chunk of the Russian population now enjoys a distinctly Soviet identity; they take the Soviet Union as their own. Meanwhile that same propaganda demonized Tzarist Russia, and nostalgia for the time of French-influenced nobility and triumphs against Napoleon is far, far weaker - especially among the working class, which can't really identify with the Hussars or Petersburg courtiers.
By escaping from the rule of a foreign power - foreign both geographically and ideologically - and then becoming (almost literally) a runaway success, the former province juxtaposes itself to the former metropoly.
Finland's success is an affront to a suppressed aspect of Russian identity. Estonia's success is an affrong to the dominant aspect.
* In response to criticism in the last post's comments - here I'm not referring to "the West" as a single political entity, but as a single concept of values, based on free market economy, representative government and the primacy of the citizen's interests over those of the state. Therefore this refers mostly to continental Europe, although in a broader sense involves Japan and Australia, who are only the West to Californians and Argentinians respectively.