Optimal trade-off between oversampling and filter length
1-d MMSE derivative filter for uniform spectral prior

With some simplifying assumptions about the signal distribution, a filter with least square frequency response error is the Bayesian minimum mean square error (MMSE) filter for a uniform prior of the frequency spectrum. For such 1-d filters, an oversampling factor $\beta \approx 2\ldots2.5$ seems optimal, as it is in the sweet spot of the cost-benefit curves (Fig. 1).

Figure 1. Mean square frequency response error of least square optimal derivative filters as function of computational complexity as measured by $\beta N$ which is proportional to the total number of multiply-accumulates (MACs), for various oversampling factors $\beta$ for which the filters have been optimized. Also shown are traces for different numbers $N$ of non-zero filter coefficients. No advantage was taken from impulse response anti-symmetry or simple coefficients such as $1$. 

More data is needed before general conclusions can be drawn.