On my QH mare I use a tom thumb, mainly because that's the only bit she likes (I haven't ever rode her in a snaffle and her previous owner said that she could spit it out of her mouth, I'll be trying her in one when I'm breaking her to drive so we'll see!). I also use a halter when we're going for a quick ride or just riding bareback (I do have a bosal but I'm too lazy/forget to adjust it to her!)
On my gelding I typically use a snaffle when we ride western or do ground work and when we're doing english I use what I think is an egg butt snaffle? It's some type of english snaffle I know that much!
I use it on him because he loves it when the rider has severe contact on his mouth (due to insecurities on his part, I don't want to seem like a cruel person who can't ride so I'm going to clarify, I don't like as much contact as he does but when you can't beat em join em right?) with the snaffle I feel it's safer to give him what he wants. And he doesn't need a harsh bit, just something to relay the contact with.