Flying Matsue - Tokyo?

After checking on the rail options, perhaps it could be better to fly Matsue-Tokyo?
The trains seem to cost much more than a discount air flight with JAL or ANA.
Is one airline preferable to the other generally?
Fares seem to be Y13000 -much cheaper than the JR pass on trains .

It depends on the airline you are using to come to Japan. If the airline is member of the Star Alliance, then you should get a Star Alliance air pass and fly with ANA from Yonago Airport. If the airline is member of Oneworld, you should use the Oneworld air pass and fly with JAL from Izumo Airport. If the airline is member of neither alliance, you will only be able to purchase an air pass that requires you to make at least two domestic flights:
http://www.japan-guide.com/e/e2364.html

Thanks.
It appears though that we can book online Matsue-Tokyo with either ANA or JAL for Y13000 each. There seems no requirement for Airpasses for this as far as I can see, or the requirement for minimum 2 domestic flights.
Must be booked min.1 month max 2 months ahead seems only requirement. We are arriving Japan on Jetstar so have no access to airpasses (Yet) so,if this is correct it is a blessing!

Yes, that is right. No air pass is required. As for which airline is more convenient: if you start the journey from Matsue City, I would use JAL, which operates out of Izumo Airport. Izumo Airport is easier to reach than Yonago Airport, which ANA is using. Some more details are on the following page:
http://www.japan-guide.com/e/e5805.html

Thanks Uji, JAL it will be.