I think ListPlot is the way to go, since you'll probably have multiple values of f[ x, y] for the same value of sqrt(x^2 + y^2 ).
f[{x_, y_}] = Sin[x y];
mod[{x_, y_}] = Sqrt[x^2 + y^2];
pts = Flatten[Table[{x, y}, {x, 0, 10, .1}, {y, 0, 10, .1}], 1];
fpts = f /@ pts; modpts = mod /@ pts;
ListPlot[Transpose[{modpts, fpts}]]
