I love BaT. I have not sold one there, but when i get around to actually putting the Imperial up for sale, it's going there. They have to approve your car; it's not just "hey, I want to sell my car on BaT, here's a shitload of pics and a description!"...it has to go through their approval process. From the time you make a submittal and to the time it's run, it could be three months or so. They will advise you right before your car runs. It costs the seller $195.00, IIRC, and that's it! The buyer pays a minimum of $250, and a max of $5,000 for the buyer's fee. Compare that to the auction houses out there, you can't beat that! They DO like to nudge sellers towards "no reserve" auctions, though.
They recently ran their 100,000th auction! Impressive, considering they started in 2014. I bought my '71 IH Travelall off of BaT, but that was back when they also ran ads off of CL to help fill their pages. I wouldn't hesitate to sell on their venue. If your feelings get hurt easily, it might not be for you. Most commentators are pretty knowledgeable, but there are a few knuckleheads.
Their current ownership has little to do with BaT as a whole. All of the original BaT people that started there are still there. It's a refreshing change from the nonsense of ebay, CL, and FB; as well as the drunken insanity of BJ, Mecum, and the big auction houses with their exorbitant fees, and more.