Russia spends a money on media outlets such as RussiaToday. Qatar has Al Jazeera. Saudi Arabia has the Saudi Broadcasting Corporation. Russia get's return in that more and more people who are delusioned with the European political class become pro-Russia. The Arabs do manage to promote their perspective of Islam being important through their media. Should the US provide a well funded news outlet like Voice of America to counter those voices and spread Western values around the world? Might it be a better value-for-money than a lot of the military spending the US currently engages in for reaching foreign policy objectives?
Voice of America may have been useful in the former USSR whose citizens did not have direct access to the western media. Back then the Voice of America and its European analogs were the only alternative to the official propaganda. These days Russians have internet access and the Voice of America is just one more media outlet with a minuscule audience. Spending money on it would not change this.
This could play in either of two ways: their editors may not be willing to sink their standards into tabloid territory enough for it to be effective propaganda (compared to an outlet like RT, for example), or they may be, in which case it would produce distaste in Western critics, who might then suggest a toning-down on the grounds that it's making us look bad.
I happened to have read a few articles about the Russian propaganda machine lately; not straight from the wolf's mouth, though, so take this with a spoonful of salt. Apparently it's the worst kind of yellow journalism. Conspiracy theories, straight-faced lies, utter bullshit, bias to the nth power. So say the analysts, at least. It works well enough to keep Putin's approval rating into the high 80s, and to create and maintain pro-Russian factions in surrounding countries of interest. (The fact that dissenting voices inside Russia tend to be murdered probably helps as well.)
I'll cautiously make the following two claims: one, any propaganda that works would have to play dirty to around this extent; and two, this shit may fly in the East but it won't fly in the West. Blatant US propaganda would be attacked both by domestic and hostile media. Any audience that's clueless enough to fall for it is Eastern enough to start out with an anti-American bias. The Russian model would not be the right one to import in this case. Better to maintain the image of Western media as mainstream and high-brow; any work left to be done consists of making it more available internationally, through translations, but also through wider distribution and through appropriate pricing.
If we're talking the spread of Western values, the cultural export industry that is Hollywood might prove enough. Keep churning out the superhero movies and other such American entertainment if you want to win support amongst foreigners.
Viliam Bur's description on LW provides a good example of what well funded Russian media achieved in Slovakia and how it radically increased the Slovakian approval rating of Russia.
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