Amiga definitely borrowed OS concepts from Mac/Lisa. I don't think it would be possible to make the case that Mac was derived from Amiga.
I owned many Amigas and they were great- especially relative to the competition at the time (DOS then Windows, and Mac included). They leveraged a number of new ideas to pack a lot of punch into relatively cheap packages... a scenario of very high value for not very high prices which- in computers of the day- was not that common.
Many of the things we take for granted in our computers today could be credited back to ideas that were first (or better) implemented in Amigas. Big color palettes, relatively good multitasking, offloading tasks to coprocessors for things like graphics & sound, running other OSs in a Window (virtual PC-type stuff) etc were relatively impressive at that time.
I recall going to one of those computer stores that carried PCs, Apples and the new Amiga when the latter first came out. The PCs & Apple were grayscale (or green or amber mono color), mono sound and relatively high-priced. Even the first Amigas demoed the famous bouncing ball in 32 colors with stereo sound. Not so long after, the Amiga demo switched to the "juggler" which was early ray-traced 4096-color animation which could run on a new version of the Amiga that could be had for just a few hundred dollars. At that time, PCs and Apple machines were still playing catch-up on some of the most tangible benefits of Amiga. Where the bouncing ball demo might have made them squirm, they had nothing to touch "juggler" for several years at anything close to the price of Amiga.
As objectively as I could look at things for several years back then, nothing touched Amiga out of the box. It's owners made a number of mis-steps in caretaking for that amazing baby which gave others time to take many steps to catch up. For example, DOS gained Windows during that time and Macs went from grayscale to color. In hindsight, I think if a company very serious about the future of computing that was also well financed had owned the Amiga, it might have become the dominant platform of the present day. There was one last flurry of huge hope when Gateway purchased it in the 90's and had a leader in charge of it that appeared very committed to finally making a serious run with it (behind the scenes though, it appeared Gateway then pulled the plug). A German company purchased it but then did little with it too.
Anyone who genuinely got to know one at the time should not be able to argue with typical biases for the other 2 platforms. As is often the case though, a better mousetrap doesn't necessarily make the world beat a path to your door.
When the Amiga "died" for me (for which rumors of a complete death are greatly exaggerated even today for that platform), the choices at the time were either Apple with something new called OS X or a 1000 variations of Windows-based machines running Windows 98. At that point in time, neither could do some things that my last generation Amiga had been doing for 4-5 years but both came with other benefits (particular mainstream software support) that couldn't be had by continuing to stick with Amiga. OS X looked like it had more potential to me than Windows, so I (at the time) gambled on Apple (which was still not so far from being on the brink of failing as a company itself). Since, I've observed OS X advances still seemingly taking some cues for how things worked on Amigas in the 1990's (whether that's true or just coincidence, I don't know of course).
Even today- 2013- there's still some things that Amigas could do that neither Windows or Macs seem to be able to do but much of what made Amigas great in their day has been surpassed in both platforms. For example, hardware 4-channel sound of Amigas seems pretty quaint now. 32, then 256 & 4096 colors vs. todays 16bit and 32bit graphics cards are similarly far surpassed.
Nevertheless, while I couldn't credit Amiga OS as leading to Mac OS in any way (I'm sure it was much more the other way), I could credit Amiga overall as continuing to have influences on both modern platforms even today. Tangible elements of Amiga superiority probably motivated both IBM and Apple to switch to color and step up all of the parts of computers that support multimedia development. Amiga's could talk with a voice not much inferior to Siri even way back then. If you were arcade game-minded, PCs or Macs couldn't touch Amiga in terms of bringing arcade experiences into the home for several years (playing something in amber or green or grayscale could not compete with much richer color palettes, hardware sprites, multi-channel sound and on and on). In short (at the time): Amiga felt like someone time-traveled into the future and bought a bunch of computing advances back, packaged them pretty cheaply and rolled them out as an alternative. The big 2 at the time seemed several years behind. When I watch that movie "Tucker" (about the car entrepreneur), it always makes me think of Amiga.
And there are still times when I really wish it would have made it as a platform as I'd love to see what a 2013 Amiga would have been like. (and yes, I know that there is still an Amiga that can be run on 2013 hardware but I'm talking about the idea of what a 2013 Amiga would be like had it got a similar level of hardware & software investment afforded to PCs and Macs for all these years, not just running the OS on generic Windows hardware)
