With somewhat limited testing of guests inside dosbox, the framebuffer drivers, including fbcon, fbdev, and 3dfx-fb, show good results in the console and in the X window server. Between those two options, the console mode seems more responsive to input than X.
In the console, the svgalib graphics library was commonly used for games, but the linux distribution would have to be customized with the proper library versions (and maybe the kernel, too). Instead, I tried SDL-based emulators in the console via the "fbcon" driver. This was a successful approach (see one of the images above).
Wine was not working well with the above slackware-based distribution, likely because of the 2.4 linux kernel. I had success with 2.6, however. There were reports that the Wine versions of that time required a particular multithreading function, but the 2.4 kernels did not commonly compile that feature in. My impression is that the 2.4 (or even 2.2) kernels would co-exist with the dosbox emulation and Wine could be built specifically for this environment. This is not a simple method to run games and not a particularly fast one either. The linux kernel is reporting the cpu at the speed of a Pentium ~70mhz, while 9x is running games 2x or 3x faster, including much lower latency in video and audio. I have been hopeful that the console would provide an alternative environment to X-based Wine. However, many of those console-based games will have an equivalent in Dos or W3.1, both running in an unmodified dosbox.
I believe danoon is working on porting Wine to SDL. There is also a report by the Wine developers that they had done something similar for win16 applications, although the software appears unreleased. Both mention the necessity of an x86 emulator to robustly port Wine (to SDL). I'm sure they are choosing the best path to port win32 games to other environments, but I have been curious if a linux kernel could be modified and customized for running Wine and whether dosbox video emulation could provide hardware acceleration. These approaches do not require a copy of 9x.
Running linux in dosbox-x has a lot of utility, but for directx gaming -- 9x inside dosbox-x is a better choice.