The letter mentions Apple by name only once, but is clearly written as a response to Apple CEO Steve Jobs' anti-Flash fusillade of two weeks ago.
Geschke and Warnock touted Adobe as a leader in what they called "open markets", and argued that their popular technologies - the PostScript page description language, the PDF format and Flash - stood for free choice.
"We believe that Apple, by taking the opposite approach, has taken a step that could undermine this next chapter of the web - the chapter in which mobile devices outnumber computers, any individual can be a publisher, and content is accessed anywhere and at any time," said the pair in their letter.
Elsewhere on Adobe's site, the company posted a message titled 'We [heart] choice', and claimed "Openness is at Adobe's core". Adobe also launched a web advertising campaign using that same theme, with banner and display ads running several sites.
One analyst said Adobe is waging the wrong campaign.
"All the talk of 'open' and 'closed' doesn't matter," said Michael Gartenberg, an analyst with the Altimeter Group.
"That might be of interest in the coffeehouses of Silicon Valley, but we've moved beyond the point where the tech-savvy insiders make market decisions. The mass market makes the decisions."
"We believe that consumers should be able to freely access their favorite content and applications, regardless of what computer they have, what browser they like, or what device suits their needs," said Geschke and Warnock.
"No company - no matter how big or how creative - should dictate what you can create, how you create it, or what you can experience on the web."
Although the row between Apple and Adobe has been simmering for some time - driven primarily by the former's refusal to allow Flash onto its mobile devices - the quarrel got much louder last month when Apple changed the licencing language of its software developers kit, or SDK.
The new licence forbid developers from using rival programming tools, including one Adobe debuted in Flash Professional CS5, that takes applications written in Flash's ActionScript and recompiles them to run natively on the iPhone, iPod Touch and iPad.
Adobe has played the 'open' card before in the increasingly-acrimonious debate over Flash on the iPhone.
Three weeks ago, Mike Chambers, the principal product manager for developer relations for Adobe's Flash platform, accused Apple of creating a "closed, locked down platform" with its iPhone operating system and associated App Store, and claimed that Flash was one of the "open platforms" that would eventually win out over proprietary technologies.
Chambers levelled his charges as he announced that Adobe would halt further development of its cross-platform compiler.
"When markets are open, anyone with a great idea has a chance to drive innovation and find new customers," argued Geschke and Warnock today.
"Adobe's business philosophy is based on a premise that, in an open market, the best products will win in the end - and the best way to compete is to create the best technology and innovate faster than your competitors."
"Again, that's an inside-the-Beltway, inside-baseball argument," said Gartenberg, and it illustrates Adobe's misguided belief that decisions over competing technologies have an impact on the market.
"But we're not inside baseball anymore. Adobe needs to show and explain what users are missing out on if they don't have Flash. And they haven't done that."
Gartenberg also noted that Adobe is alone against Apple in the battle for hearts and minds, and argued that was another mistake on its part.
"We haven't heard anything from any other voices," Gartenberg said.
"Adobe needs to get more people on board, whether that's developers or mobile platform makers. It has to be more than just Adobe."
Some iPhone developers have expressed unease or disgust with Apple's decisions to bar Flash from its mobile devices and block the use of Adobe's cross-compiler. But there's been no widespread public outcry from programmers.
"I'm interested in creating the best product out there, and using the best tools to create that product. Right now, that means using Apple's tools," said Jonathan George, the CEO of Boxcar, a company that produces push-notification software for the iPhone.
"Frankly, it's Apple's ballgame, and [if] someone else doesn't like it, they can get off the field and go sit in the stands."
"The only way this will work is if Adobe can convince Apple's customers to put pressure on Apple to make a change," said Gartenberg.
"But with Apple selling a million iPads in just 28 days, Apple must be feeling pretty good about its position."
See also: Adobe responds to 'thoughts on Flash'