Eeesh, those bag-o-flies are so disgusting, but they work. This summer the fly problem was overwhelming. i tried the fly predators (which seems to make a big difference). Also use those fly jars (like the bags only opaque so you don't have to see all those fly eyes). Then if we were having guests over and wanted to clear the area fast, we laid the sticky fly strips all over the ground in the areas we saw the most flies.
i looked at those bug zappers but never bought one. The thing we found with the sticky fly strips, is that they don't work if hung up, they need to be on the ground as that is where the flies hover. So i would think with a bug zapper it would be the same thing. You might need to position it on the ground to catch the flies.