Adobe has just rolled out a new Web-based advertising campaign, which declares its love for Apple but not Cupertino’s policies. The new ad campaign, which states, “We ‘heart’ Apple,” comes with a caveat. While the company may have a fondness for Apple, the campaign goes on to declare: “What we don’t love is anyone taking away your freedom to choose what you create, how you create it and what you experience on the Web.

The Web ads come concurrent with a new open letter from Adobe founders, as well as a full-page ad in the Washington Post. The letter, which was co-signed by founders Chuck Geschke and John Warnock, espouses the virtues of an open Web and the necessity of translating that experience to mobile.

“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,” the letter states.

This most recent retort comes as part of the continuing back-and-forth between Apple and Adobe. In its most recent SDK license agreement, Apple banned all apps created on third-party software from being ported to the iPhone, iPod touch and iPad. 

Apple CEO Steve Jobs even went so far as to pen an open letter to Adobe, in which he outlined the reasons that Flash is not a good fit for Apple devices.

“Perhaps Adobe should focus more on creating great HTML5 tools for the future, and less on criticizing Apple for leaving the past behind,” Jobs wrote.

Adobe CEO Shantan Narayen categorically denied most of the allegations posed by Jobs, the majority of which were technical concerns. Narayen has maintained that Apple’s reasons for rejecting Flash have nothing to do with technology and everything to do with politics.