Which everything you have read and are going to read are all opinion with no facts possible.
When it comes to speakers , there are no right or wrong answers , opinions can be strong but some which actually have experience can carry some weight but not enough for you do decide which is the right way for you to go.
With all that being said the 2 brands you are comparing are excellent choices. For the money either side can argue who is better. I will also offer you my opinion on this matter from personal and professional experience.
B&W probably make hands down the best speakers in the business dollar for dollar. I completely disagree that they are overpriced as they can be magical and I've seen owners first hand with joy in their eyes and hearts after owning them. Years later still have that sparkle in their eyes every time they sit in for a listen.
Up and down their repeated lines over the years , have done nothing short of amazed and dazzled it's owners.
What they also do extremely well is be used as a double duty speaker. They shine for both music and movies. Stong clear tone up and down the scale with accuracy many can''t claim.
Triad is a custom built speaker designed for theater use. They are designed for the custom integrator in mind. They really shine in theater rooms built in and in room. They provide a theater like performance and you pay for it. They also have some of the very best theaters around the world equipped with their speakers and rightfully so.
If you do some research on them you will quickly learn that they are amazing on all levels and you do pay for that performance. Worth every penny I might add.
Both companies require really good gear to go with them with the right amount of power and control. Weaken this part of the chain and neither one of them will provide what that where designed to do.
I can't see going wrong either way here as both speaker companies are remarkable in their own respects. Both have loyal followers and both have earned that.
My only suggestion to lean one way or the other would be if music was my first choice in speakers , I would go with B&W , if theater was my first choice I might lean towards Traid as they offer very custom solutions to custom theater rooms. B&W also have many built in solutions which can be argued can compete with Traid on all levels.
I would not say Traid is better then B&W. I would say B&W can better Traid in many ways but thats an opinion of a professional and should be taken as such.