I doubt you could ever prove the two are the same, but statistically you can estimate the probability that they are not different.
Your ‘graph.fig’ file contained all the ‘YData’ information necessary. (This was something of an adventure in handle graphics for me!)
After getting the data:
hs1 = subplot(2,1,1)
hs2 = subplot(2,1,2)
x1d = get(get(hs1,'Children'),'XData');
x2d = get(get(hs2,'Children'),'XData');
y1d = get(get(hs1,'Children'),'YData');
y2d = get(get(hs2,'Children'),'YData');
the easiest statistical test was the correlation coefficient:
R = 974.4480e-003
P = 94.3711e-168
or an infinitesimal probability of no correlation.
A chi-squared test between y1d and y2d might yield definitive information because it compares each observation in y1d and y2d, and gives the probability that the ‘patterns’ between them are different. (When I did these calculations, I got chi-square = 1055.5 with 233 degrees-of-freedom, essentially a zero probability that they are different.)