Most brands make multiple styles and quality levels of catchers gear. For chest protectors, the more expensive models typically feature a better quality foam - a type that will "deaden" the ball better. If you press your fingers into them, the indentation stays longer. This gives the catcher better ability to keep blocked balls close in front. You don't want "stiffer" as the ball will deflect further away. So, it's not the brand, but which model within the brand. Also, getting one that fits best is critical.
Many young catchers/parents buy chest protectors too big thinking this will provide more protection and growing room. You want adequate protection, but you also need a close fit and mobility.
All helmets are properly safety approved (NOCSAE) - as someone mentioned earlier, lightweight and visibility are key. Again, this usually is dictated by price more than brand.
As far as MLB exposure, that's a player contract issue and does not dictate one brand being better than the other. Some brands such as Rawlings and Nike are more willing to pay pro athletes to wear their gear than others.