Lattice vs. Random sampling for function interpolation

Question

Suppose $f: [0,1]\times[0,1]\rightarrow \mathbf R$ is smooth. I am to interpolate the function from the function values of $f$ at $n^2,\, n\in \mathbf N$ samples points. I have the freedom to pick either the uniform lattice points $\big\{\frac i{n+1}\big\}_{i=1}^n\times\big\{\frac i{n+1}\big\}_{i=1}^n$ or $(x_i,y_i)_{i=1}^{n^2}$ uniformly randomly distributed in $[0,1]\times[0,1]$. Then I can use various interpolation methods to estimate $f$ at any arbitrary point $(x,y)$. Which sampling method is "better"? What constitute "better" for interpolation is part of the question.