I am not an expert, but I imagine that given the primary mission of the IDF in dealing with Palestine, they probably receive training and some experience (depending on where they are assigned) in how to spot potential terrorists using behavioral profiling. So when they leave and join airport security, they hit the ground running.
US soldiers on the other hand probably aren't given much behavioral profiling training. We seem to specialize in blowing stuff up, steamrolling it with tanks, then randomly throwing money at it afterwards. If any military or ex-military know differently, please correct me.
Gen. Petraeus may be slowly improving that SOP, in Iraq and Afghanistan at least, but I'm not sure how much his work there is getting rebased to general boot camp and officer training programs. Eg, are these kinds of soft skills percolating throughout the US military, or are only the Special Forces and other groups specifically tasked with winning hearts and minds in Afghanistan getting this training?
So the question remains, would filling the TSA ranks with military veterans and paying them higher wages provide a more Israeli-like airport security force? Dunno. Certainly worth considering, but there are some significant differences.