Home4all6 - the thread that 2LittleFishies linked discusses some of the differences between batch feed and continuous feed, but I will list them specifically here. Also, this choice is individual to the user - there is no right or wrong choice, just one of preference. Both types have pros and cons.
A batch feed disposal is turned on and off by its cover, which also doubles as the sink strainer, or if you want to fill the sink with water, the cover acts as a sink stopper too. Because the disposal can only operate with the cover on, some consider it safer than a continuous feed disposal which is turned on by a separate switch. I remember a rental apartment I lived in where the undercabinet light switch and the disposal switch were next to each other, and you really had to think before turning on the disposal. If I had children who like to play with switches and the like, I would only get a batch feed disposal. Just MHO.
Another advantage to a batch feed is that there is no need for a switch in your backsplash or a hole in your counter (for an airswitch). Love that. Also, as mentioned, batch feed disposals don't need the rubber flange that was the original subject of this thread. You can also see clearly down into the disposal to retrieve spoons or whatever that have dropped down, and no need to slide your wrist past a slimy flange.
The thread that 2LittleFishes linked mentions that batch feeds might not turn off or something like that. We had batch feed disposals growing up, and I have lived with numerous different ones over many years, and never had that happen.
The linked thread also mentions that Insinkerator batch feed disposals use a magnetic mechanism in the cover to turn on and off the disposal, and that this magnet may take fiddling. For that reason, I prefer the Waste Kings, which simply have a little mechanical notch (also mentioned in the linked thread) just inside the top drain that turns on and off the disposal. I much prefer that, and also the Waste Kings have larger chambers which I prefer too. The Insinkerators are quieter so that's the tradeoff.
In the linked thread, Marcolo mentions not wanting to have to put your hand into a filled sink to turn on and off a batch feed disposal. That would be true, but I, like others who responded in that thread, haven't encountered that situation. I mean, if you are filling a sink with water, regardless of whether you are using a batch feed disposal or not, you will have to reach your hand into the water to pull out the stopper to let the water drain in any case.
One reason people don't like a batch feed disposal is that you put your scraps into it in "batches". I.e. fill it, turn it on with the stopper, pull out the stopper, fill it again until finished. A legitimate complaint, and you have to weigh that against the other pros of the batch feed and decide what you'd like. The Waste King batch feeds have larger chambers, so it take a lot to fill them, so you don't need to do as many batches. Note that it is important to make sure you have room under your sink for the larger chambers of the batch feed disposal.
I hope that answers all the questions. It's one of those personal preference decisions.