I think it really can make or break a shave, initially all my efforts were concentrated around razors and blades and I have found the combinations that work well for me. Although I still do a little experiment with a new combination from time to time I am pretty settled on the blades and razors front. Once I got that right I have been working on understanding how the brush and soap (and technique) affects the shave.
I have had great shaves with both expensive and cheap brushes (both boar and badger but not tried horse yet...). The main difference I notice is how much I enjoy using them, 90% is technique but even well practiced techniques to build a good lather can go wrong for a whole host of reasons.
I agree with Fido, a great shave is about getting all the elements right and enjoying the whole experience, like a chain it is only as strong as it's weakest link. A good blade will not compensate for crap soap mix and good soap mix will not protect you from razor burn if you have at it like a butcher in a bad mood.
I personally find badger easier to work with and more luxurious to use, it is a preference not a rating or scoring. I have proved to myself that I can get a fantastic lather with boar but I know that I just enjoy a good 2 band badger brush and have a growing collection of them, each with their own personalities and requirements to get the best out of them.
For some this trial and error is a pain but for me it is that voyage of discovery that is the fun part.