I do not know which Linux windows system is slow & why. But making K-meleon faster on Linux seems to have been talked about before, to quote an ex-contributor to the K-Meleon project about possibilies to run it better from on nix:
I'm just an end user myself, .... a few points of interest...
While K-Meleon is officially designed for and supported on only MS Winows 32 bit operating systems, unofficially it can most likely be run on *nix using the WinE abstraction layer (i.e., run with wineexec), as KaZaA, UltraEdit and other native windows MFC apps can be run under WinE with no real problems. Also, once winelib has full MFC support, most likely a *nix ELF binary can be produced by linking to winelib at compile-time. Both of these methods would be unofficial and unsupported, to say the least. There is also a cross-platform GUI toolkit called WxWindows that supports almost all of the MFC functions and has an almost identical syntax; someone more talented than I may one day port K-M to WxWindows, and then it would be able to be compiled from source on any OS that supports WxWin (which is currently like every 32 bit OS).
If i recall correctly, I have had a look at the windows version of mfcembed.exe made with WxWindows & runs as well as the real mfc application. AFAIK mfcemebed is the ancestor of k-meleon with version higher than 3 or so. This project sometimes uses emfembed for testing. There is an embed project for Linux also.