Try this:
axes(handles.axes1); % Switch focus to axes1.
theImage = getimage(); % Snag the image out of axes1.
axes(handles.axes2); % Switch focus to axes2.
imshow(theImage); % Place theImage into axes2.
If you want to make more compact, you could skip axes() and pass the axes handle into getimage() and imshow() but then to get other things, like title() etc., to appear on the correct axes you'll have to pass the handles into those functions too. If you call axes() things like titles will appear on the current axes (the one you just passed into axes() function).
