You're Wrong!!! (lol)

There are a few key points. First and foremost you can not approach the problem as B is better then A. Better is an opinion. There is no way to say "better" that doesn't come off like opinion. Instead focus on the projects goals. If the goal is to make 500 sales, then prove, with real quantifiable numbers that B will have more conversions then A.

For an example, one client I work with has a horrid looking site, that is difficult to use, and hard on the eyes. Anyone coding or designing the site would try to push it towards a "better" design. However, the site exceeds their current goals. They convert sales much better with an ugly, hard to use site, then they do with a nice clean design.

Next, remember that it's their money. If they want to pay you to implement a bad design, that's their call. It's your job to lay out the fact that it's a bad design, but it's theirs to make the decision on using A or B.

Finally, keep in mind that the "best" design is the one that meets the users' needs. A lot of times I see people go "flavor of the week" on site/app designs, when it's not the best design for the project. Sure a certain method may be more user friendly, but look down at your keyboard. QWERTY is by far not the "best"... and yet...

So, the main approach to take is that "You're Wrong" and you need to prove you're right. Prove that B is better then A using real quantifiable numbers. If you can't then you're still "wrong", and all you're doing is trying to force your opinion on them. If it comes right down to it, it's their money and they can always give it to someone else.

P.S. - Right and wrong in this answer are meant to demonstrate a clients feeling. You may very well be correct that B is better then A, but that's not going to stop the client from feeling like you're wrong, and that you're trying to bully them into doing it your way.