I have seen a test ,on another forum, by a TV engineer. He stated that a bat wing is actually the best at distance reception provided has the "wingman" retrofit addition. (all the new ones come it std) What the Jack antenna does is be less directional and you can be more "sloppy" pointing it at the station antennas. You get that at the expense of it not reaching out as far, less distance from station.
a couple points You may know already Know ...... there is no such thing as a HDMI antenna. Thats pure Marketing. Its VHF or UHF as it always has been and when tv stations went digital many (most ) stations went UHF which doesn't go as far as it cant pass through objects or terrain as well. what you need is a good UHF antenna and thats what the wingman attachment does as does the Jack.
One caution is I did have a friend we had camped with have a Jack on his trailer ripped off by a limb as it does stand up and not lay flat. but avoiding limbs is a good idea anyway