I was thinking that the beta Stirling engine would be the most efficient as it has a displacer to block heat transfer from the hot to cold regions in between thermodynamic cycles. However, I heard that the alpha engine has the best power-to-weight ratio. Of course, that doesn't necessarily mean it provides the greatest output of power from the same amount of heat source.
I'm not really considering the gamma type, as there is too much dead volume that makes it inefficient.
With the alpha type, I'm concerned that there might be unnecessary transfers of heat in between cycles without displacers. I mean what stops the heated air from escaping to the cold side and vice versa?