To be honest Dosbox does a pretty good job of handling the cd for me. (about the only exception I can think of is Heroes of Might and Magic 2. On an old version of dosbox it never played the cd music, and on 0.63 it crashes when I try to use the cd music. Too lazy, and not interested in playing it at the moment, to bother trying the CVS to see if it's been fixed.)
If hasn't been fixed in the CVS and low-level CD access in Linux is what you're after, you might want to try dosemu.
The game support seems, at least to me, not quite as good as dosbox (haven't tried the latest versions, to be honest though) and the setup is nowhere near as simple as dosbox. To enable the cdrom in dosemu, I had to obtain a dos CD-ROM driver, set-up the autoexec and config to load the driver properly, and enable the cd in the dosemu.conf. Can't say whether it's gotten any better.
On the other hand it ran HOMM 2 with the CD audio, and it reads the CDs even when I don't have them mounted.
Your call. Personally I'd try the cvs of dosbox first.