I use the JP Korsteel oval mouth eggbutt (https://www.smartpakequine.com/jp-korsteel-oval-mouth-eggbutt-6148p?utm_source=Google&utm_medium=googlepla&utm_content=TES&utm_campaign=2109694282&cm_mmc=Google--googlepla--TES-_-2109694282&source=pla&gclid=CjkKEQjw5LWcBRCeh8uUlqqluN4BEiQAfr64cEzuzrF4yqkNsYewDDh5AsfysbHI1NTXlvOBi4ivu27w_wcB) on my Arab or a mullen pelham when I ride with a bit (I ride him on trails and endurance rides in a sidepull that’s a glorified halter). He doesn’t ever need a pelham for brakes or whatever. I use one foxhunting on really formal days mostly just for the traditional look. I chose the snaffle just based on what bit he went well in and didn’t fuss with. I tried a lot of different bits and that just happened to be the one he liked the best. I’m on board, its inexpensive enough I can easily put the same bit on several different bridles.
I’ve never needed something with ‘brakes’ on him. He’s got a very soft mouth and he’ll slow and stop off of seat cues.
My mare goes in a “jumping hackamore” (https://www.horseloverz.com/product/bridle-parts/190910-tory-leather-jumping-hackamore.html) or a rubber mullen snaffle. Both chosen because the morons I bought her from nearly severed her tongue in half with who knows what and she strongly objects to bit pressure from anything else.