Are anime more popular in terms of viewership and revenue than Western cartoons? I was wondering if anime are more popular than Western cartoons - in terms of viewership and revenue - as I couldn't find any information on this. 

I don't think there has been any significantly large survey on this. What about manga vs comics?
No. Up until now Japanese anime have never been in the popular spotlight compared to works for Western animation. Anime can be described as a &quot;pulpy&quot; format, often cheaply made, heavily-formulated, low critical respect and scrutiny. Though what makes anime unique is it's meta-genre. There are a lot of ideas in it's story templates the that are not typically seen or are non-existent in Western media culture.
Animation in the West
A lot of Western animation companies, like Disney for an example, don't just treat their works as a product, but as a brand. The better their brand looks to consumers, the better marketability the company will have with related works and products (they spend a lot on PR, marketing, lawyers, focus groups, etc, to ensure this). There's a lot of oversight involved is western animation, in order to ensure a better quality product, which typically drives up the cost of production. Of course, this all to ensure that their product is a successful as possible, in order to make obscene amounts of cash.
Animation in the East
While there is a ever growing community of anime fans out there, who like anime for one reason or another (e.g., characters vs. story), but few people typically care about the specifics of anime. In anime, the stakeholders are more concerned about the overall final product than any given piece of it, the product hits the main selling points of the formula (e.g., fighting, boobs, robot, X-dere character, harem cast, etc.), it's good to go. With anime there's a general lack of oversight, which typically leads to low expectations of the audience and from them as well. However the pulpy aspect of Anime allows authors a much higher level of freedom as they are free to explored new ideas, as long as they meet the initial criteria of the stakeholders.
On Popular Culture
This pulpiness is the same as what webcomics (modern comic book heroes starred in this pulpy format) and indie games are to us in these modern times. There are tons of these all around, most of it is forgettable, but occasionally there's that polished gem that can really good interesting, funny, charming and/or inventive stuff (e.g. Azumanga Daioh, Serial Experiments Lain, Baccano!). There's a lot of opportunities to fail, learn, and innovate, but at the same time the barriers for entry are lower and turnover is usually higher compared to similar works of western animation.
Viewership and revenue are often a by-product of the popularity of a given brand. Just like really popular mainstream movies or games will always make a profit, no matter how good or bad it might be (e.g., the Call of Duty series, the new Transformers movies). Western animation has built a brand image and following through it's popularity, and in order to sustain it's overwhelming popularity, there's a lot of scrutiny from both the audience and stakeholder to maintain a certain image and status within popular culture. We don't typically see this with anime, so it gives us an idea that anime specifically is not really up there in the mainstream.
Nowadays we see a lot of people on TV and the Internet proclaiming themselves to be &quot;geeks&quot; openly (whether they are or not is another thing), so there's not a whole lot to be said about anime and the otaku subculture. One can say they are a gamer (&quot;I'm a huge gamer&quot;) or a TV show/movie (&quot;I'm a big Disney/Pixar/Spongebob/Avatar fan&quot;), but there are very few people come out about anime. This leads us to believe that anime hasn't reach the tipping point where it can be considered acceptable, like the other forms of western animation.