I would plot them with surf and then look at each separately and then both together, depending on what they are (here, plotting the differences).
For example —
f = @(x,y) exp(-((x-1.1).^2/3 + (y-1.5).^2/4));
g = @(x,y) exp(-((x-1.2).^2/4 + (y-1.3).^2/3));
xv = linspace(-5, 5, 50);
[X,Y] = ndgrid(xv);
figure
surf(X,Y,f(X,Y))
title('f(x,y)')
figure
surf(X,Y,g(X,Y))
title('g(x,y)')
figure
surfc(X,Y,(f(X,Y)-g(X,Y)).^2)
title('(f(x,y) - g(x,y))^2')
A statistical test would depend on the matrices themselves and the how best to describe the differences.
The last plot calculates and plots the squared differences, and it is not obvious to me what statistical test would be most appropriate.
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