I used amithlon/os3.9 as my main system for years. Winuae is nice in it's own way, and has the advantage of also having custom chipset emulation (amithlon is rtg/ahi only), but for my tastes it's never felt quite right and amithlon has always been the better experience. It has less hardware support, but with a little shopping around its not too difficult to get a fully supported system, even with modern gear. No host OS is required (well technically Amithlon is the host OS (a customised linux kernel) , but its minimal to a point of never being seen). It's both faster than Winuae and unlike Winuae everything is done from within Amiga OS (drivers, uses amiga os tcp/ip stack,etc.). It's also possible to use native x86 amiga os3.x software from within 68k AmigaOS (although not a lot has been compiled for this architecture) for even more speed. Even when my a1200+bppc+grex1200/voodoo3/256 meg fast system was functional I found Amithlon to be the best OS3.x experience. As for what advantages either bring over classic hardware it mostly comes down to just performance, which in turn opens up new doors to OS3.x.... high res video files run flawlessly, duke3d, quake, quake2, freespace, napalm, and many other pieces of software that even the most expanded classics might struggle with run nicely, various emulators (mame, megadrive, super nintendo,playstation,etc.) all run great, sdl software is suddenly more than usable, compiling times drastically improve, lots of room for OS enhancements (afa os,etc.) without hurting performance, 3d rendering software is drastically faster and so on.... in short imagine a classic amiga with an '040 running at speeds 20x (and then some(sysinfo tells me I have roughly a 3.5ghz '040, but to be fair synthetic benchmarks and emulation dont always represent the true tale)) than that of the fastest '060. To suppliment the lack of custom chipset emulation there's also a 68k version of euae (I simply set up a def type to launch adf images with euae), although if you have a classic amiga already this may not be so important (although I also at one point ran my classic through a tv tuner card inside amithlon/os3.9)..... on an even modest pc you get 680x0 speeds in excess of what any available OS4.x hardware can provide for native ppc software. This is mostly true of Winuae as well, but if your interest in a pc is soley for what it brings to the amiga table Amithlon is the way to go in my opinion (assuming you can find it of course, as its no longer sold).
Now having said this it took a while, but AROS has gotten to the point where it's a serious alternate option. It doesnt run amiga software out of the box, but janus uae can create a fairly seemless intergration with things like launching software as normal from Wanderer (AROSes Workbench), aros menus for 68k software, mixing aros and amiga os software as though all native (cycling through screens with the screen gadget, etc.), full screen or windowed apps and so on..... a different method to either os4 or mos, but quite effective nonetheless and the advantage of full emulation and not just system friendly stuff. As nice as it is to have this however the real benefits of something like AROS (or os4.x/mos) is it's more modern software. Although there's probably no software that either have that couldnt be done for os3.x the simple fact is that it seldom is done and often if it is there's not nearly as much time/effort put into OS3.x versions of more modern software.... things like movie players, web browsers, sdl software (Of which there's a lot(although only a small percentage is decent in my op.)), 3d/gl games are all better experiences on the "NG amiga" systems.
Personally I still very much enjoy a lot of classic software and for all the advantages the NG systems offer I cant do without an os3.x system. Having said that though the same is true of the reverse.
