For me it's boar, all day every day. But I am a function over form, plain-jane Ford pickup, no frills, brass tacks kind of guy. I like stiff brushes, unscented soap, scalding hot water and shave with a straight pretty much exclusively.
Stoneandstrop and I have discussed this before and gentlemanly take opposite corners with due respect. I have the same Omega 48 and find mine quite soft as boar goes. Actually three is a cheap (cheap among the cheap category) chinese boar brush I buy on fleabay for the knot for reknotting old handles because the bristle is so stiff. I have tried badger and found it too soft. I understand the appeal but it's not for me. Mainly it seems the method is different. Badger is good if you like to push the brush into your face. It requires a sort of mopping action. Boar is too stiff for that. It requires more of a paintbrush sort of action. But in my estimation, for whatever method you choose the aforementioned brush works best to suit it.
As with most things I find that what you learned with is likely what you prefer. My Dad always used boar. Maybe that has something to do with it.
I have never tried horse but from what I can tell from having handled them they are not for me.
I don't fault anyone for what they use but I just can't wrap my head around plastic brushes. It just feels...wrong to me. I can't explain it, just wrong.
Enjoy what you like because you like it, and more power to you. Shave on.