The conflict that Philipp emphasizes is mostly between NATO and Russia. Of course since most EU members are also NATO members, that may seem a "duh, obvious" conclusion: EU is in the same conflict with Russia as NATO is, but EU (unlike NATO's) expansionist moves in what Russia sees as its "sphere of influence" have been more limited, and vary by EU country:
The Eastern Partnership, in which partner states are meant to eventually sign a free trade agreement and a wide-ranging association agreement with the EU, was conceived of by Polish Foreign Minister Radoslaw Sikorski in 2008. It was built as an offer of closer relations with six countries of Eastern Europe and the South Caucasus—Armenia, Azerbaijan, Belarus, Georgia, Moldova, and Ukraine—following the Russia-Georgia war of August 2008. [...]
Germany’s support for the Eastern Partnership was always halfhearted at best. Merkel provided some rhetorical backing before the November 2013 Eastern Partnership summit in Vilnius, Lithuania, calling on Russia to accept Ukraine’s sovereign right to choose its alliances. But neither Berlin nor other big member-state capitals sent clear signals to the Kremlin that the EU was ready to confront Russia over the right of countries in the post-Soviet space to associate themselves more closely with the EU.
When Moscow began to put pressure on Ukraine and Moldova in summer 2013 using embargoes and bans, the EU failed to respond in a resolute way that might have convinced Russia that the union and its powerful member states were ready to make Russia pay a price for sabotaging the Eastern Partnership. When Armenia suddenly stopped its process of EU association in September 2013, apparently under pressure from Moscow, EU leaders just shrugged; no EU government made an effort to change Yerevan’s mind. And the promise of EU accession—the strongest carrot—has never explicitly been offered to Eastern Partnership states (it hasn’t been excluded either, though).
The EU has two vital interests at stake in the current conflict with Russia. First is a stable and prosperous neighborhood in the East. The second is Russia’s respect for the ultimate taboo of Europe’s peace order—the prohibition against changing borders by force. For a bloc that is founded on accords between states, upholding the rule of law in international agreements is vital. And to see a powerful country invading and annexing the territory of a weaker neighbor for Europeans brings back memories of a darker age of ruthless competition.[...]
Still, the EU remains very reluctant to move with full steam toward a confrontation with Russia, for a number of reasons: Economic ties are strong, especially in energy, finance, and the arms industry. Western European countries are less concerned about Russian aggression and want EU attention to instead move toward the Southern neighborhood. Some EU members fear being confronted with a Russia that appears to be driven more by emotion than by rational considerations. And European governments cannot ignore sections of the public that sympathize with Russian action (partly driven by values that they feel are supported by Russia, partly driven by the wish to balance U.S. influence by moving closer to Russia). [...]
In the struggle over Ukraine, both sides have lost illusions, about themselves and about the other. The EU understands now that it has to back up foreign policy with substantial power—in a world that is much less “postmodern” than Europeans have hoped for in the past, a world that still largely looks at the international system in the terms of classical power politics. It also understands that Russia is not interested in the kind of partnership Europeans—guided largely by Germans—have proposed for two decades. [...]
Russia, meanwhile, has found out that it is much less attractive to states in the neighborhood, especially in Ukraine, than it had hoped. And it has learned that when faced with a vital challenge, the EU can be a much tougher opponent than the Kremlin might have expected: EU member states, under German leadership, have managed to uphold a credible threat with massive economic sanctions for months, and they have built and upheld a common approach with the United States.
So basically Russia wants an EU that isn't strong enough to oppose it politically in a major way, especially in what it see as Russia's "sphere of influence" (mostly post-Soviet countries)... but Russia also has some conflicting interests in maintaining some EU market access etc. And EU countries also perceive this conflict. So your (gerrit) observation/assumption is basically correct: simplistic analyses that Russia automatically gains by anything going bad in the EU... are just that... simplistic analyses.
But clearly Russia has given support (even if just verbal) to European movements that seek a rapprochement (a less harder stance toward Russia), typically populist movements, e.g. the latest alliance that won power in Italy or LePen in France; Russian support for the latter was more than vebal. But regarding Brexit: it's not clear that Putin has taken a side in that (although some lesser Russian figures have), but what is more clear is that some Brexiteers (declaratively) favored better ties with Russia, well... until they came to power, anyway.
And what I said about simple analyses can probably be summarized by this snippet from the last article linked:
Moscow's Mayor Sergei Sobyanin believes Russia wins from Brexit.
"Without the UK in the EU, there will no longer be anyone so zealously standing up for sanctions against us," he tweeted.
Konstantin Kosachev, the head of the upper house of parliament's foreign affairs committee, admitted to Life TV: "Considering our difficult relations with the EU, there is a temptation to gloat over the EU's misfortunes."
But Mr Kosachev himself resisted the temptation. He pointed out that the EU remains Russia's largest trading partner.
"If the EU falls apart at the seams," he warned, "this will affect our trade relations".
