IMO BAT is better than eBay in that BAT has more "real" buyers because they automatically charge the winning bidder their fee as soon as the auction is over, resets the auction clock at 2:00 after each bid so there are no BOT or fake bids at the end, and has more interaction during the auction. However, most cars listed on BAT are super/exotic cars and not classics/muscle cars so your buyers are not the same market as Mecum/BJ. BAT fees are also way more reasonable than any live auction like Mecum/BJ, you don't have any transportation fees, and your auction lasts 7 days not 45 seconds.
I sold my '70 Cuda 392 Hemi on BAT and had a good experience with their photographer (a contractor for BAT). He picked a great spot, had the list of required photos from BAT, edited and uploaded all photos. BAT will ask you questions for the initial write up, they will send you a draft to edit it before the final listing. BAT will also ask what you want the reserve at and then negotiate it down based on previous sales of like make/models/years. Then BAT will then tell you when your car will be listed, likely a couple of weeks out.
Once your BAT auction starts I have found the best auction results include a very active seller, meaning you have to respond quickly and accurately to all questions, post comments or additional features to highlight your car throughout your auction, and post additional photos and videos at least once a day because people who tag your auction as "watch" receive emails/texts for any additional photos/videos posted and this keeps your auction at the top of their list. BAT will tell you to not post when your reserve is met or close, but some sellers do anyway. I'm not sure if this really impacts the sale or not.
When your auction is over and the reserve was met, BAT will put you in touch with the winning buyer and it is up to you to make arrangements for payment and transportation. If your reserve is not met, BAT will still put you in touch with the highest bidder to see if you can negotiate a deal. Again, something eBay does not do. If there is an issue with payment or the winning bidder does not full fill their purchase, BAT will ban that buyer and offer to relist your car for no additional cost.
This is a great video comparing Mecum vs BAT -