If you care about the models under the hood, keep reading. if not, skip to the end for some recommendations.
The almost universally use the same physics - the Point Mass method, which is the standard method you'll see engineers using for this sort of thing. It's just F=MA. There are a couple exceptions. Hornady uses a slight tweak to the standard PM, which is slightly useful at long range (but you rely on them for the data which is doppler based and also calculated). Applied Ballistics uses PM, but uses doppler drag data which is a big deal for ELR. AB gets at the same stuff that Hornady does, but with a slightly different method that's a good enough and requries less data.
Patagonia claims to use a proprietary "aeroballistics model" based on Pejsa and Kallman filters (which does not make any sense at all). The obsolete Pejsa method is a simplification of the PM method that is less computationally demanding at the cost of accuracy. Modern computers eliminate the need for that. Kallman filters are totally unrelated to to ballistics, and are a way to make estimates based on multiple data sources of varying uncertainty. They don't explain this at all. This strikes me as marketing BS, but that doesn't' mean it doesn't work. I wouldn't know because it's insane to pay for it.
Trasol doesn't tell you what they are doing - if memory serves, it was also Pejsa, but they may have changed it. I haven't really kept up. Looks like it has a nice UI. They also chose to go with the "proprietary" marketing BS, which annoys me.
This stuff is just basic physics that was figured out many decades ago - there is no "proprietary".
Practically speaking, the results you get should all be basically the same out to 1000 yards. Pick based on bells and whistles and what you're willing to spend.Personally, I would either use a free PM calculator, or if you're shooting ELR, the AB calculator (because of the data).
Shameless plug: I use mine - a free, online standard Point Mass calculator.
A free ballistics calculator for long range shooting.
bisonballistics.com