Pool boiling of refrigerants is a primary heat transfer mode in flooded evaporators, as well as a promising solution in electronics cooling applications. In this work, the pool boiling performance of R-134a, R-1336mzz(E), and R-1336mzz(Z) on the external side of round tubes are reported and compared to Cooper's heat transfer coefficient (HTC) model. Modification of Cooper's correlation is found to be necessary for R-1336mzz(Z) at low reduced pressure. Micro- and nanostructured tubes are tested using the three different refrigerants and are shown to enhance the boiling HTC. Specifically, three various structures consisting of: boehmite (AlO(OH)) nanostructures, etched aluminum microstructures, and copper oxide (CuO) micro-nanostructures are fabricated on the external sides of aluminum and copper tubes. The surface structures have characteristic length scales of 100 nm, 1 µm, and 10 µm for boehmite, CuO, and etched aluminum, respectively. While the boiling HTC is enhanced up to 250% (compared to smooth tubes) using R-134a with etched aluminum, it shows a 15% decrease in HTC when boehmite structures are used. For CuO, higher heat fluxes showed a 25% HTC enhancement, while lower heat fluxes showed negligible effects when compared to smooth copper tubing. Different refrigerants showed various relations between structure and HTC enhancements. To take account of both structure length scale and refrigerant properties, we introduce a normalized structure size (Rn) and conclude that HTC enhancement ratio increases non-linearly with Rn. Our study not only provides valuable data on refrigerant pool boiling of recently developed low global warming potential and ozone depleting potential fluids, it also provides valuable design guidelines for the development and application of micro- and nanostructured surfaces in chiller and electronics cooling applications.