My Batwing amp died, so I swapped that head for a Jack, since it was on sale. Works fine. No issues with roof obstructions either.
I can't say for sure if the Wingman gets longer range, but a neighbour with one was getting some stations that I was not, one time I checked. (But this is not science with lots of data) Within range of the Jack , got lots of stations, no problem. Somewhere over 50 miles and it gets tricky it seems. Some stations are stronger so you still get those.
If you are in trees, nothing can help much. Luck of the draw what you can get.
One thing is whether you have to use the wall wart that comes with the alternative antenna amp, or if you can use your rig's old Winegard "12v" to the antenna. It turns out you can just use the rig's 12v and not have to use the wall wart on inverter. The amplifier is not fussy about the exact amount of "12v"
Another thing is if you have one of those coax amplifiers, you can't use it with the antenna amplifier and amp the amp. Doesn't work at all. Your antenna amp is all you can get.