Today, there seems to be a lot more recommendation s for using teflon lined hose for transmission lines than there used to be.
We know that modern gas will eat up conventional braided hose due to the ethanol content. After about a year, you can usually smell the seepage even if you don't see the leak due to evaporation.
Historically, braided line has been rated for hydraulic fluids which includes transmission fluid. I notice more and more sites are suggesting teflon lined hose for long life when used as cooler lines. How much of this is marketing and how much is long term experience, I have no ideal. We know some rubber lines used for transmission coolers will get soft and swell after some period of time. Braided line does not contain rubber but another compound developed years ago.
One of the problems with the teflon hose has been that it did not bend in tight radius's and the fittings were a pain in the neck. I know there is hose available today that will bend more sharply but I have not looked into the fittings.
I suspect that if you buy a name brand hose that is not chinese in origin, either one will work...but, it's expensive compared to steel line and hose.
On my Challenger, I used steel lines to the front of the car and then I used push lock hose and AN fittings to plumb a cooler.
Guess it's time to do some more reading.