I think you are talking about general compatibility and not games, so my thoughts:

Dosbox - no, because its lacking printer support (except for special builds) and share support, especially office software will have problems. When you "boot" an Dos 6.22 image in Dosbox you will at least have share. 800x600x256 is working nicely on it.
Wine - I'm not sure whether 16bit programs are its strong point

I'd go with VMWare and VirtualPC but these have shortcomings as well and might not work the best with win3.1x...

Hmm. DOSBOX is not intended to launch Win3.x and Win9x, although I'm testing it intensively and...it works! Of course with bootable image, but I've tested some games (Earthsiege 2, Command & Conquer Gold, X-Wing 95, Civnet,TFX). All works, although not all games play CD-AUDIO tracks...but I think DOSBOX is a good plattform to emualte even Windows environment. Of course, VPC and VMWare are more efficeincy, but also less compatible (for example - C&C doesn't launch on both dthese emulators, and under DOSBOX/Win95 - works. But you have free choice 😀

Wine is not an option, as it does not support 256 color modes, except for some oddball hacks that usually don't work (Note that programs can run; Oregon Trail 2 runs fine IIRC) . Win3.1 has always worked well in DOSBox for me; I run Myst in it all the time. Don't know much about other VMs though, except that Win95 in Virtualbox do not work very well (At least, Sonic CD had trouble 😜 )

Just to clarify, yes, Dosbox is perfect for games, be it Dos or Windows 3.1x games (and I *think* the future looks bright for Windows 9x games). And even for most applications it is mostly good. Only when you need printer support and share (the OLE stuff in Windows 3.1x needs that) you should stay away from Dosbox.

What exactly is "share"? Some DOS function that is not emulated in DOSBox?

Oh, and thanks for giving your opinions.

http://en.wikipedia.org/wiki/SHARE.EXE does not work on Dosbox which is no big loss for games. Windows 3.1x uses a Windows version of this vshare.386 and this is needed by many office programs, especially by MS (Office programs, Works, Publisher...) but also the Lotus stuff needed it (AFAIR) and it is used for multitasking, embedding files from other programs, essentially OLE http://en.wikipedia.org/wiki/Object_Linking_and_Embedding .
Without share these programs will either not start or not function properly.
Older versions of Dosbox hid the fact that share was not working and thus these programs did run but the use of the share function did not work. Now the programs will see that right away 😀

One of game, Earthsiege 2, refuses installation without enabling sharing. This was cause, which forced me to make a bootable partition with Windows 3.x. Otherwise, I couldn't play this game.

In general, Virtual PC 2004/2007 is best for DOS + Win3.1. You can use either VPC 2004 or 2007, but you'll want the DOS addons from 2004.

Also see here. Virtual PC and VMware Workstation DOS memory management