My family and I have been a frequent flyer and EVA lover on Taipei-U.S. routes. But a recent incident really pissed me off (something happened on the plane but the way the handled the situation afterward really blew my mind) yet I don't think it's appropriate to disclose anything at this point.
Actually it matters. And I suggest you tell us anyway - there is no need to be afraid. It is known that a lot of airlines (but not CX and BR yet) have official representatives to listen people in here.
(As a matter of fact, I had once complained about no water to use in the lavatory (empty water tanks) for SFO-LAS from pre-merger Continental - now UA. And I joked about how they compensate the situation in here. Guess what? Continental Corporate Office read the whole thing...
...and we ended up with an interesting conversation...)
The reason why it matters is you want to switch because you want to avoid the issue from happening again, right? So let's play devil's advocate - if CX has done something in the past, will you still switch or not?
Regardless - switching or not is entirely up to you. BR is on its way to *A, which in that case, a stronger network. BR's program will need to be changed as well due to re-alignment with *A program. These change may not be as pleasant as they will be seen.
CX - as it is now - faces a lot of challenges, like aging fleets, cost-cutting, devaluation of loyalty, and so on. Realistically, if you switch to CX, you (and your parents) will end up spending more time on the road (due to the extra TPE-HKG segment). Even those the price may be the same (for the sake of this discussion), how much is that extra time worth for you? You will have to take it into consideration as well.