Apple does not compete with Adobe over technologies like Flash. Apple's decision to leave Flash off its multi-touch devices is based on (according to Apple) the instability of Flash and the power drain Flash causes on portable devices.
The lack of Flash on the iPhone has been a realm of contention between Adobe and Apple since the iPhone launched in 2007. Now things have heated up again, since Apple's just-released beta version of the iPhone OS 4 SDK license bans ported Flash, Java, and Mono apps. A primary feature of Adobe's forthcoming Flash Professional CS5 is the ability to export Flash content into the native iPhone format. While Adobe has officially so far remained mum on this, their platform evangelist (who apparently had to be reined in by corporate, after his initial post did not include adequate disclaimers) has told Apple to "Go screw yourself."