Beats vs. Bose

One problem with your question is it is too broad. Beats makes several models of headphones and so do Bose. Are you looking for on the ear? Over the ear? Ear buds, Inter-ear monitors (IEM)? Wireless? Completely wireless? Do you need sweat resistance?

I've had the Powerbeats 2 and 3 and while they were okay I wasn't thrilled with them and ended up selling them. I've never found any Bose that I liked but others swear by their noise reduction. Not read good things about their wireless IEMs.

I have a friend who has the Beats Studio Wireless and loves them around the house. Her husband has a set of MEE Audio Cinema Matrix BT headphones that I gave him and he prefers those. She prefers her AirPods Pros at work. Her brother prefers the Powerbeats Pros. I absolutely abhorred the sound of the original Beats Solos but the models 2 and 3 are much improved and quit over supplying the bass. If you love bass you will prefer the Beats over the Bose by far.

As to other makes, models, I've really been happy with what I've bought from MEE Audio, they aren't fancy looking but they work great and have good sound especially for the money. I also like Ultimate Ears (and someday I'll get an ear form done and order a custom set), Grado, B&W, Bang and Olufsen.

Neither.