I mainly use a badger brush that I got for $10 from Ebay at Hong Kong. It's as good as my $50 Edwin Jagger badger brush. It does a good job with all shave creams, with all shave sticks and with most soap pucks.
But there are some soap pucks where the soap is just a bit harder, and I get frustrated trying to get a thick lather using the soft badger brush (L'Occitan's Cade is one such puck). With those, I use a cheap boar brush which has harder bristles, and I instantly get a good lather. I've noticed some of those soap pucks got lousy reviews at Badger and Blade, when they gave me excellent shaves - providing I used a Boar brush.
For me, the other main difference is that with a boar brush, you feel that you are sort of massaging your face, as you can pummell the brush into it - something you can't really do with a badger brush.
Given I'm very happy with my $10 brush, I haven't explored the world of the $150+ silver tip badger brushes, and I haven't seen any horse hair ones available here to tempt me.