I'm looking to save up for the soon to be announced line of updated Macs and I'm interested in two particular models, the iMac and Mac Mini. I've been hearing for years the the Mac mini provides superior sound quality even with an external DAC because there is less noise than a laptop or an AIO like the iMac because the lack of a built in display. How true is this statement?
While I do see a lot of Mac Minis at Hi-Fi events, it producing less noise than an iMac with an external DAC doesn't really make much sense as the audio itself isn't coming from an external source.
Short answer: No.
Longer answer: No, you're making too generalized of a statement (or are being told too generalized of a statement) - there is no "universal iMac" or "universal laptop" - there are literally thousands of different designs, with different components, builds, etc that constitute "all laptops and AIOs" so you can't generalize like that.
Even longer answer: You need to separate AIOs and laptops in the discussion. Laptops can run from battery power, or AC bricks, and its not uncommon on many models for folks to report background noise when running on the AC brick, but "dead silence" from battery operation (I've owned one such machine, a Compaq, and I forget the rest of the model - it was years ago; running on its AC brick there was a very slight hiss/hum on the analog outputs, but running on battery it was dead silent). Beyond that, PurpleAngel is right that with an external audio interface (e.g. FireWire, USB, etc) or DAC (S/PDIF, ADAT, etc) you're bypassing all of the internal analog audio circuitry, which *may* pick up noise or be problematic (audibly) in a computer (*in any computer* although in more recent times this is becoming, IME, the minority of systems). There's also a lot of hyperbole and blatant BS that goes on with audio gear and audio review magazines, and its gotten worse since computers have come into the equation, one of the biggest myths is "more expensive is MOAR BETTAR!" and its not at all surprising when you find articles where folks take "cheap gear" (e.g. a Mac Mini) and it doesn't kill their dog, burn their house down, etc but actually provides audibly transparent performance (or near audibly transparent performance) and of course they're going to rant and rave about how magical it is "for the price."
I would say buy whatever computer that ultimately fulfills your needs/requirements as a computer, try out the built-in audio, and if there are issues with its performance, there's a cavalcade of devices that range from quite affordable to hilariously priced that can bypass the onboard audio. Given that you're specifically (exclusively?) looking at Apple, I would also provide the standard disclaimer that you should wait at least a month after whatever their "new hotness" launches for all of the bugs, problems, etc to be meticulously documented and complained about by Apple diehards, and hope that at least some of them are fixed/resolved (and before anyone accuses me of being biased against Apple - the same reasoning applies to new releases of Windows, except I would say wait a year instead of a month).