The problem you're having is improper correspondence between your axes. I think you're presuming that the loop is a known good example, but it's not. This loop:
for i = 1:length(x)
for j = 1:length(y)
z(i,j)=exp(-(abs(y(j)/7))).*sin(x(i))+exp(-(abs(x(i)/7)))*cos(y(j));
end
end
produces Z data that's transposed WRT x and y. The only reason this doesn't throw an error is because x and y have the same length. If you change y to say
y=-6*pi:.2:6*pi;
then you'll get a nice error because x,y, and z have mismatched geometry.
Error using surf (line 71)
Data dimensions must agree.
If instead you use
z(j,i)=exp(-(abs(y(j)/7))).*sin(x(i))+exp(-(abs(x(i)/7)))*cos(y(j)); % note LHS subscript positions
the plots will work without error, the two versions will match, and the x and y orientation matches the axis labels.
FWIW, i'm assuming the only reason you're making two identical plots is to try different methods of generating the Z data. While it's often more convenient to use meshgrid, it can also be done with the x,y vectors themselves.
z=exp(-abs(y'/7)).*sin(x)+exp(-(abs(x/7))).*cos(y');
This is elementwise operations using one row vector and one column vector. This works by generalized implicit array expansion post-R2016b. Prior to that, the same could be done using bsxfun().
