One simply cannot compare a Batwing, Jack, or frankly any other directional RV antenna against an Omni-directional antenna. They have no gain, and are fraught with problems receiving multi-path (echo) from buildings, water tanks, canyon ducting, etc.. I could fill the page with examples of problem objects that render these antennas useless.
I was at our new, less than a year old TV station this week in San Antonio, walked in and asked who installed an omni RV antenna in the roof next to my $300,000 tower with $600 antennas OTA antennas on it, and got an earful about some hair-brained idea someone had.. The install was beautiful but received only one station in one of the largest cities in the nation. I have plenty of experience with these things on ENG News trucks too and feel well qualified to say they are useless in any service. If you can use one at the house, it does what you need and never moves, great. But it's by far the worst idea for RV service.