CMD.EXE is the Windows NT's native command prompt (or shell), which means it is more portable among different hardware platforms. For example, if you type SET and press ENTER inside a CMD.EXE prompt, you'll notice that CMD.EXE exposes more environment variables than COMMAND.COM. On the other hand, COMMAND.COM is the more "MS-DOS compatible" version of the two shells. For example, this shell will call AUTOEXEC.NT and CONFIG.NT (located in the SYSTEM32 directory inside your Windows NT directory) just like MS-DOS used to call AUTOEXEC.BAT and CONFIG.SYS.
So, if you're having trouble running your old DOS command line programs from Windows NT, try running them inside a COMMAND.COM shell, not CMD.EXE.