The Little Tarheel HP is the better antenna for a this size. Not because it handles more power, but because this antenna uses far less tuning coil for each band compared to yours. For this reason, this antenna requires an external antenna matching coil to bring up the lowered feedpoint impedance while yours does it within the antennas tuning coil itself. The matching coil losses are minimal since it's at the feedpoint. One drawback for some to the HP model is that it's only tunable down to 40 meters with the standard whip. 80 meters on a mobile is less than 5% ERP anyway so it isn't a big deal for me.
Your antenna can do 80 meters with no external matching which means that antenna uses way more loading coil to tune than the HP model on 40 meters meaning very low efficiency due to big losses in all that loading coil being used. The more coil used to tune, the more the ERP goes in the tank!
IMHO, the Little Tarheel 2 is just an efficient leaking dummy load! Think about it, 6 thru 80 meters for an antenna no longer than a typical fiberglass CB antenna and requires NO antenna matching? Just plug and play is why I believe people choose this model.
W9CLL makes a good point that a longer whip will improve it some but you will likely lose 6 meters and the longer whip you go you'll start losing 10m and beyond.
I'm using the HP antenna with a fairly rigid 5 ft steel whip., This let's me tune down to 60 meters and still has an inch or two of coil left. I did lose 6 meters but that''s OK because bands above 20 meters use far less tuning coil to tune meaning improved efficiency over the stock flimsy whip. I can easily just switch out the whip if there is a worthwhile opening on 6m.
Unless you desire 80 meter mobile operation, I would return that antenna and get the HP model if your mobile operation requires using a smaller size screwdriver antenna. I can and easily do 80 meters on my HP with a 17 ft telescoping whip on it but obviously this is when I'm stationary. This will effectively increase the ERP not only on 80 but bands up to 20 meters!