We had a bat wing and it was OK. Then we added a Wingman ($25) and it was much better. Then we had a problem and it had to be replaced. We went with the Jack this time ($50 replacement head) and it is just great. Much better reception and does not need to be aimed as before. Our experience shows that the Jack is superior. That said, there are certainly places where no antenna will work.
There are 3 batwings, Sensar II, III and IV.. The Jack looks to be right about a Sensar III
If you have the basic Sensar,, (That's the II, the original Sensar I is no longer made)
Add the Wingman, 30 bucks (I think) and it's now a Sensar III and just about equal to the much ballyhooed jack.
Then add the Sensar Pro indoors modult, This replaces the wall plate if you have one or if not goes BETWEEN the antenna and the box of many buttons. That makes the III into an IV which does a much better job.
HOWEVER... If that's still not good enough, and you are parked for a long time, consider putting up a mast.. And on top of the mast put a deep-fringe antenna with mast head amplifier by Channel Master or some other top antenna company.
Also.. SOME of the mast head amps may be compatable with the Winegard power supply (The indoor module weather a wall plate, sensar pro or BOMB is the power supply) and able to use the original Roof top ANT line This may or may not be an advantage, else bring it in on the CABLE lead.
Height is might on VHF and UHF, I proved that years ago.. But I've told that story before ask if you need to read it again.