Military man
From a Licensed airframe / engine engineers point of view I think you would be better off taking the avionics course, thats of course assuming you wish to gain 'hands on' employment.
In order to satisfy todays JAR requirements then a mechanical man has to now re-train in electrical systems (B1 license) to enable full certification responsibilities. Avionics, without provoking an argument, is probably the superior trade within aviation line maintenance. however, if you wish to pursue a career in design then the option of mechanical would be the preferred choice as stress engineering and srtucture evaluation is far more interesting.