Like stated above it is hard to beat the BATWING antenna. The JACK antenna probably is a tad better gain wise but with all the simple tests I ran here at my location looking at WASHINGTON DC digital Natl Broadcast TV Transmitter Stations that are situated on both side of DC I finally decided the BATWING was still the best for me.
The KING is apparently more NARROW BEAMED meaning you really have to point the antenna right at the transmitting station where the BATWING has a larger BEAM WIDTH. Both antennas did the same great reception for me here in Northern Neck Virginia some 50 miles away from the DC area. The BATWING was able to pick up both groups of the WASHINGTON DC transmitters with a single pointing angle. I could not do this with the JACK. Had to move the antenna everytime to pick up all of the NATL BROADCAST CBS-NBC-ABC-FOX-PBS HDTV signals... My test antenna setup was on 15-foot PVC pole in clear view towards Washington DC.
I have never used the Jensen ANHD20 OMNI-DIRECTIONAL antenna but the reviews don't give it a good rating.
I have played with one of these WINEGARD HIDE-AWAY ONMI-Directional DUAL DIPOLE antennas which also does not perform very well... It is a great PLAN B back antenna however... RABBIT EARS sitting on the roof is also a good back up antenna...
The best antenna I came up with was one of these DB8 BOW-TIE antenna DUAL PANELs using four BOWTIE antennas in each panel. The one I used each panel can be be positioned. This works great for the house setup but not a good antenna to mount on top of a RV for mounting reasons. Antenna Direct and Solid State Xtreme Signal (AMAZON) are a couple of sources for DB8 antennas.
Roy Ken