I appreciate your answers. I went over many papers that discussed these differences between the methods. what I have in mind is the following: few papers stated that 'it is advisable to use SFA in the case of one output and multiple inputs.' without referring to a reference.
The paper Multiple input-output frontier analysis – From generalized deterministic to stochastic frontiers by Andreas Dellnitz Andreas Kleine can be a good reference
COLS ( corrected ordinary least square) is also used.
It seems to me (I am not a specialist) that DEA works well if the hospitals you wish to analyse face the same institutional and economic environment. SFA is more flexible when some external constraints are specific to some hospitals and not to others (kind of "fixed effects" in panel regressions). It may be the case if they are in different regions with different sets of administrative rules. My two cents...
This a lot debate on this question not just for health systems efficiency but on when to use which. Nonetheless, most studies I have come across use SFA as opposed to DEA...
I did estimate the data again by DEA and the correlation between the SFA & DEA is significant with some discrepancies in the ranking.
The data used in the paper include small and large hospitals and urban and remote areas hospitals. this may justify using SFA; the noise in data is a determining factor.
The method you can choose based on your consideration of functional relations between input and output. DEA provides less restrictions to functional priori compared to SFA. Both methods have advantages and disadvantages. But DEA have a variety of models that can useful for your analysis in more depth information.