Yes there is. It's called maths. You'll need to know the Young's modulus ("stiffness") of the two materials you want to compare, the geometry of the frame and the dimensions of all the tubes, as well as the point you intend to apply the force and the direction you intend to apply it in (i.e. is it flex under pedalling, or under the weight of the rider that you're wondering about?).
Since a lot of frames these days are made of oddly-shaped tubing, it's likely to be really quite complicated to work all of this out, but it's a fairly simple principle. It'll give you the deflection in the frame for a given force.