Is there any statistical method to compare two curves? Is there any statistical method to visually compare two curves?
What is the best and correct way to compare two similar curves and calculate the error/difference in percentage?
I have created a program that generates a curve of a column base using Bezier curve. Now, I want to find out how accurate my generation is. So I have a function for the first curve I defined, but I dont have a function for the second one, which is only on the picture.

 A: A standard way to compare two (sufficiently nice) functions $f(x)$ and $g(x)$ over the interval $[a,b]$ is to use the inner product $$\left<f(x),g(x)\right>:=\int_a^b{f(x)g(x)\,\mathrm{d}x}$$ from which we get $$||f(x)-g(x)||=\sqrt{\int_a^b{\left(f(x)-g(x)\right)^2\,\mathrm{d}x}}$$ where you can think of $||f(x)-g(x)||$ as being the "distance" between the functions $f$ and $g$.
If you are dealing with parametric curves you could use $$\text{dist}\,\left(x(t),y(t)\right):=\sqrt{\int_{t_0}^{t_1}{||x(t)-y(t)||^2\,\mathrm{d}t}}$$ to get a reasonable measure, but you would have to ensure that both curves are parameterized in the "same way".
EDIT: If you want a measure of "percent error" I suppose you could do something like $$\text{% error}=\frac{\text{magnitude of error}}{\text{original magnitude}}=\frac{\int{||x(t)-y(t)||\,\mathrm{d}t}}{\int{||x(t)||\,\mathrm{d}t}}$$ which is the integral of the difference divided by the arclength of the original path. Since you only have points, you would have to approximate by computing $$\frac{{\Delta t\over 10}\sum{||P_i-B_i||}}{\sum{\sqrt{(x_{i+1}-x_i)^2+(y_{i+1}-y_i)^2}}}$$ where $P_i=(x_i,y_i)$ is the $i$'th point on the path and $B_i$ is the corresponding point on the Bezier curve. So if the Bezier approximation is parameterized with $0\le t\le 1$ then $$B_i=y\left(i{1\over 10}\right)$$ where $y(t)$ is the curve.
Keep in mind that I'm making this up as I go ;) But hopefully you can work with some of these ideas and see if anything fits what you're wanting to get...
A: I think the best way is to overlay the new curve over the old one - such as putting the new curve on paper and laying it over the old curve.  Do this on floor, or on a window pane to create a transparency effect and then take a digital caliper (or similar - ruler, etc.) and measure the offset between the two curves at as many points as you can. 
The differences are your error. Make sure you record whether they are positive or negative, and as absolute value, as you may want to look at both total error and/or average error. Average error should be around zero if the new curve is proportioned correctly.
