The version of the kernel you are running doesn't directly effect the stability of MythTV, since MythTV runs outside the Kernel. However, many of the TV card drivers will run in the kernel. When deciding, please read your driver's requirements. Obviously, the stability of your system overall will depend on the stability of the kernel which is the heart of the OS.
There are currently 2 major versions of the Linux kernel in use:
The latest versions of this kernel are really stable. That fact can be rather important for a PVR.
This kernel rather, so it may contain drivers for your hardware not available in the 2.4.x branch. It has a new process scheduler made for desktop interactivity, it is not clear if this improves MythTV usability or not. The introduction of the "CFQ elevator" in kernel 2.6.6 might also be interesting, since it is tweaked for multimedia applications. It will try to minimize the time programs need to wait for data from the harddrive, which should result in snappier FFW/RW.