I believe you're mainly talking about this popular Oatmeal comic strip that went viral.

There is actually a Forbes magazine article that dispels some popular myths about both, Tesla and Edison. Quoting some of it here:

The Oatmeal strip goes on from there, thankfully moving away from the mindless Edison bashing and discussion, in brief, some of Tesla’s other achievements. Of course, during this part, he mostly gives short shrift to a lot of the brilliant scientists and engineers who developed things like wireless communications, remote controls, and other things. This isn’t to say that Tesla didn’t have a big hand in a lot of these inventions – he did! But a lot of other people worked on them, too. They built on Tesla’s initial work, advanced it, and developed practical inventions. That’s how science and engineering works. The inventors who came after Tesla built on Tesla’s work, just as Tesla built on the work of Faraday, Pixii, and countless others.

The comic also makes the probably false claim that Tesla had developed a practical means of wirelessly transmitting power. He certainly claimed to be able to do so. But there’s no actual evidence that he did. Tesla was just as prone to self-aggrandizement as anyone else. Especially in his later years.

What’s more, there are a two things that the Oatmeal didn’t comment on that I think are worth mentioning. For one, Tesla claimed to have observed cosmic rays traveling faster than the speed of light. They don’t. He was famously skeptical of relativity, but his criticisms have since proven unfounded.

Of course, I just highlighted one point from the article, but it is worth the read. The internet loves to lap up the underdog. Matthew Inman (creator of the Oatmeal comic) just painted a picture of Tesla that would be appealing to most of us. Making Edison 'look like a dick against a great mind' probably added to the image.

The reality is, Edison and Tesla were colleagues, and apart from a few misunderstandings, largely remained amicable. If anything, Edison (who heavily backed DC systems) and Westinghouse (who ultimately did buy the patent for AC transmission from Tesla) had a rivalry, known now as the 'War of Currents' around the late 1800s. The only reason Westinghouse won is because AC is ultimately more practical and cheaper than DC transmission, especially over long distances. Tesla seemed like an indirect rival (since he did hold the original patent to AC transmissions, though he did try to convince Edison to switch) which is where I think the whole 'Edison vs Tesla' flare-up on the internet arises from. Edison, in hindsight, just backed the wrong horse.

There is no mention of Edison uttering 'you dont understand american humor', or at least I cant find any. It should be important to note that Edison, while being an inventor, ran a business. Most of his actions (that have polarized views right now) as a result, need to take this into account. Many humorous accounts exist of him electrocuting a prisoner on death row and an elephant (that was meant to be put down anyway) which gets marred into a hate campaign against Tesla on most forums. Fact is, even till 1890, most people then didnt know which form of electricity to back, and Edison merely had such publicity stunts to try and garner support.

Feasibility won. Edison didnt foul-mouth Tesla, as is the impression you might get from popular opinion.

Full article here: http://www.forbes.com/sites/alexknapp/2012/05/18/nikola-tesla-wasnt-god-and-thomas-edison-wasnt-the-devil/

Edit: added an explanation after /u/Bernardito pointed out

Not to discourage other responses, but there have been similar questions before, specifically in regards to his behavior towards Tesla, and in my opinion, /u/khosikulu killed it just like Edison did that elephant!

The gist of it is that the rivalry - if there was any - was probably very much overblown by a biographer of Tesla, named O'Neill, in the 1940s. But go read his whole answer!

There are very few instances of isolated "genius" in science and engineering.

First, nearly every single advancement in the state of the art is built on the smaller achievements of dozens, if not hundreds, of people who came before them.

Second, an advancement is useless unless it is adopted by users. I could invent free energy and warp drive in my basement and it would be functionally useless unless I had a team of marketers and salesmen to spread my inventions to the masses.

Edison was a brilliant man who was the master of taking and productizing inventions and getting them in the hands of people.

Tesla was a brilliant man who was the master of taking the advancements of people and pushing them just a little bit further.

But the whole "Edison vs. Tesla" feud is silly.

Tesla isn't the originator of even half the ideas he is credited with, and mythical stories of lost or suppressed technologies swirl around him like religious tales. If you look at Tesla's patents and products, every single one of them was a refinement of someone else's idea-- and for some reason that really riles people up. Even the eponymous Tesla Coil is just a slightly redesigned and refined version of the Ruhmkorff coil, an invention that predates Tesla's by 40 years (and which was itself a refinement of someone else's invention).

Edison wasn't the man who single-handedly built the future. He was a skilled businessman who aggregated technological advances and enabled their widespread adoption. If you look at his inventions, every single one of them was a product of a team of scientists and engineers.

As far as being dicks, they were both dicks. Edison screwed people out of money and had a pretty evident disregard for the health and welfare of his workers. Tesla was a eugenicist who took investor funds and used them for his own personal projects, and he was a dick to people he thought were unattractive or biologically inferior to himself.

Follow on question:

I heard that the reason the film industry in the states is concentrated where it is, is because they had to move there to get away from Edison's bully boys smashing their equipment. Is that true?