Warning - potential long winded opinated post...
Interesting thread, with some nice POV's being expressed.
But, the original question needs a tweak. Instead of asking which OS is best at multitasking, perhaps it should be which OS is best for a given task requirement.
Why? Because we are comparing an OS that hasnt been developed - really - in, what, 15 years? (I dont really call WB3.5 and 3.9 major developments over 3.1, and the ROM hasn't changed at all), and a hardware platform that hasn't changed in terms of horsepower or capabillity in just as long.
On the other side, we have Windows, which can trace a heritage back to VMS, but is "only" 4 years old, and Linux that is, well, constantly developed and comes in a zillion flavours. And the hardware platform that can be 10 years old or 10 weeks...
And thats before we take into account the custom chipset that the Amiga has, which allows the OS to offload tasks from the CPU. Not only is the OS different, but the hardware is completely different. The PC OS expects the CPU to do everything, AmigaDOS doesn't. Ok, so the PC has GPUs... these didnt really come of age until, say the advent of the Nvidia G-Force Yes, I know there have been grpahics accelerators for the PC since the 80s, but these really relied on optimised CPU drivers. One could argue that is still the case, as a driver is still needed for the latest video card or physics processor, there is no native OS support in the kernal/HAL for graphics off-loading. Why- because the architecture "floats"; the PC I buy or build is different to yours, so the modular approach has to be taken. An Amiga is an Amiga is an Amiga. A PC isn't, well, not to the same degree.
Its like asking which car is "best"; this Datsun 380ZX from 2002, or this one from 1987. Put them in a straight line race, and the older car wins. But is that best? best at what? best fuel economy? Comfort? value for money (however the heck one measures that highly subjective phrase!), and so forth. Now add in BMW M3s from the 80's, 90's, and lastest series, and ask a BMW fanatic which is best... Oh, and maybe Hamman M5/450 for interest (540 series with a 5.5l engine from an 8 series shovelled into it...)
See what I'm getting at? There is no single reference point to make a comparison.
Theoretical discussions about the elegance of a particular OS approach to multitasking fall flat when hardware is factored in. In turn, that isn't an absolute statement, but one which works pretty well in the real world.
AmigaDOS and OS2/3 is "better" than XP? it may or may not be, (lets say it is). But on what hardware platform? It can beat XP into a crooked hat on paper, but I'd rather be using XP on a dual Opteron with a few gigs od RAM than an A500 with 1mb and a single floppy... the time saved between the two systems booting is wiped out in the time spent using Final Writer to type a letter than Word. And I can play MP3 on the XP box at the same time... cant on the A500. Yes, I could have protracker or wahtever running, but I doubt I'll find my music in that format.
Ok, so I use an A4K with PPC/060. Final Writer runs a bit faster. ProText runs quicker, but a character based WP on a GUI system... nope, still give me Word.
Yes, I do believe that AmigaDOS does multitask "better" than XP, and have used the floppy format analogy often. I've also used, as a challenge to annoying peeps that boast they have the fastest&meanest rig that my computer can do a task quicker than theres, and I'll stake my rig on it; the task is to write and print a letter. I'm using a Commodore64 with Easyscript cartridge.... its "fast". But I wouldnt use it for a mail merge! (why? ever doen mail merge from a very slow floppy drive! Yes, I could add a REU and HD, but the expenditure outweighs the benfit of a few simple text only letters. Adding GEOS in, it gets s.l.o.w again)
The theory is fine. But like all theory, it cannot take into account that wonderful thing called the real world. You have to take into account the hardware, and what one actually wants to accomplish.
In a way, its linked to the "polls" one used to see in printed Amiga magazines, "what would you like to see in a new Amiga". Well, when you look at many of the answers, what you end up with is not an Amiga.
Examine what one wants to do, then decide what apps offer the fucntionality to achieve that, which decides the platform.
AmigaDOS is still best. even though I cant use multi-monitor display, have no simple IP stack, slick browser, decent email client, slick graphical UI... otoh, Pagestream 3 rocks! I'm not even looking at PS on the PC...
just my long winded tuppence.