The first version of the iPhone's OS had a brutal process management approach not unlike PalmOS, as I recall -- with the exception of bits of the system apps, if the app wasn't on screen, it wasn't running.
And that really changes the equation. There's a completely different notion of performance and memory management because you don't have multitasking. There was no window management, no interprocess communication, no unix subsystem. (Essentially no text selection and no copy and paste!)
So it wasn't "running Mac OS X"; that was a red herring. It was running a Mach kernel and a big chunk of Cocoa.
My guess is that people at Palm would have understood this right from that first demo.
And it wouldn't for example have been surprising to anyone at Compaq, because the iPaq series at that point was producing not-too-dissimilar devices in terms of power, able to run Linux and X11 while multitasking.
Likewise it wouldn't have surprised anyone at Nokia that here was a very powerful device with a high resolution screen and a pretty much desktop-capable webkit browser that played streaming video and audio, because Nokia had already shipped a device with some of those characteristics and shipped it 14 months earlier; like many in the UK and Europe I had a webkit-capable 3G device in my hand on the day the iPhone was launched (an E61) and had been using it (and testing websites on it) for months.
So what Apple had done on a technical/OS level wasn't so mindblowing if you knew your way around the decisions others had made, and had a view of the devices on the market (outside the USA where it was seemingly Windows CE or nothing). They were ahead, but they weren't so far ahead as for it to be completely unbelievable.
They had made careful choices and tuned the device for them.
(Seriously: no copy and paste until 2009, right? No 3G.)
The difference was -- as it always is with Apple -- execution.
People (including me!) should have been paying more attention not to this sort of OS-level achievement but to the design and delivery of the UI and apps. Serious thought had been given to capacitive touch and multitouch, which Apple didn't invent but did perfect, right out of the gate.
The CPU performance, the OS technicalities, whether it was OS X or not, didn't sell it to _anyone_. Indeed, Apple confounded anyone interested in features over benefits -- it didn't support third party applications.
What sold it was that it was understandable and comfortable.
> Those first versions of OS X were not snappy.
I ran OS X on day one of the public beta, on a blue and white iMac, and I don't recall its performance being bad (apart from the absence of sound). I remember it being amazing. But it's important to note that OS X on a Mac was a very different operating system; a fully preemptive-multitasked, multi-window OS with a BSD subsystem, IPC, swap, etc. etc., and running on hard disks, not flash.